%% bibtex-file{ %% author = {Alexander I. Suciu}, %% date = {December 26, 2012}, %% filename = {bibserver.bib}, %% url = {http://www.math.neu.edu/~suciu/bibserver.bib}, %% www-home = {http://www.math.neu.edu/~suciu/}, %% address = {Department of Mathematics, %% Northeastern University, %% 360 Huntington Avenue, %% Boston, MA 02115, %% United States of America}, %% telephone = {+1 617 373 3899}, %% fax = {+1 617 373 5658}, %% MR = {168600}, %% genealogy = {37530}, %% ftp-archive = {http://www.math.neu.edu/~suciu/papers/}, %% email = {a [dot] suciu [at] neu [dot] edu}, %% dates = {1984--}, %% supported = {yes}, %% supported-by = {a [dot] suciu [at] neu [dot] edu}, %% abstract = {Bibliography for Alexander I. Suciu}} % ====================================================== @COMMENT{meta_data, INDEX = {META}, TYPE = {Personal bibliography}, AUTHOR = {Alexander I. Suciu}, AUTHOR_URL = {http://www.math.neu.edu/~suciu/}, AUTHOR_ID_MR = {168600}, TITLE = {Publications of Alexander I. Suciu}, HEADING = {Publications of Alexander I. Suciu}, AUTHOR_LIST = {http://www.math.neu.edu/~suciu/publications.html} } @COMMENT{author_data, AUTHOR_DATA = { Babenko, Ivan K. id_mr:28790 http://higeom.math.msu.su/people/babenko/ Cohen, Daniel C. id_mr:290411 http://www.math.lsu.edu/~cohen/ Denham, Graham id_mr:343377 http://www.math.uwo.ca/~gdenham/ Dimca, Alexandru id_mr:58125 http://math1.unice.fr/~dimca/ Dwyer, William G. id_mr:61120 http://www.nd.edu/~wgd/ Falk, Michael J. id_mr:225576 http://www.cet.nau.edu/~falk/ Farjoun, Emmanuel Dror id_mr:59915 http://www.ma.huji.ac.il/~farjoun/ Friedl, Stefan id_mr:746949 http://www.mi.uni-koeln.de/~stfriedl/ Jekel, Solomon M. id_mr:94210 http://www.math.neu.edu/~jekel/ Katz, Mikhail G. id_mr:197211 http://www.cs.biu.ac.il/~katzmik/ Klein, John R. id_mr:308817 http://www.math.wayne.edu/~klein/ Kreck, Matthias id_mr:106415 http://www.hausdorff-research-institute.uni-bonn.de/kreck Matei, Daniel id_mr:652915 http://www.imar.ro/~dmatei/ Papadima, Stefan id_mr:190377 http://www.imar.ro/~spapadim/ Plotnick, Steven P. id_mr:140405 Schenck, Henry K. id_mr:621581 http://www.math.uiuc.edu/~schenck/ Suciu, Alexander I. id_mr:168600 http://www.math.neu.edu/~suciu/ Yang, Yaping http://www.math.neu.edu/people/profile/yaping-yang Zhao, Gufang http://www.math.neu.edu/people/profile/gufang-zhao }} @misc {Suciu:fs12, author = {Friedl, Stefan and Suciu, Alexander I}, title = {K{\"{a}}hler groups, quasi-projective groups, and 3-manifold groups}, MRCLASS = {20F34, 32J27, 57N10, (14F35, 55N25, 57M25)}, keywords = {$3$-manifold, graph manifold, {K}\"{a}hler manifold, quasi-projective variety, fundamental group, {A}lexander polynomial, characteristic varieties, Thurston norm.}}, abstract = {We prove two results relating $3$-manifold groups to fundamental groups occurring in complex geometry. Let $N$ be a compact, connected, orientable $3$-manifold. If $N$ has non-empty, toroidal boundary, and $\pi_1(N)$ is a {K}\"{a}hler group, then $N$ is the product of a torus with an interval. On the other hand, if $N$ has either empty or toroidal boundary, and $\pi_1(N)$ is a quasi-projective group, then all the prime components of $N$ are graph manifolds.}, ID_AR = {1212.3022}, gsid = {3220684310602343222} } @misc {Suciu:ds12, author = {Denham, Graham and Suciu, Alexander I}, title = {Multinets, parallel connections, and Milnor fibrations of arrangements}, MRCLASS = {32S55,55N25 (32S22, 57M10, 18D50)}, keywords = {Hyperplane arrangement, {M}ilnor fibration, characteristic variety, orbifold fibration, cyclic cover, multiarrangement, multinet, deletion, parallel connection operad, polarization}, abstract = {The characteristic varieties of a space are the jump loci for homology of rank 1 local systems. The way in which the geometry of these varieties may vary with the characteristic of the ground field is reflected in the homology of finite cyclic covers. We exploit this phenomenon to detect torsion in the homology of Milnor fibers of projective hypersurfaces. One tool we use is the interpretation of the degree 1 characteristic varieties of a hyperplane arrangement complement in terms of orbifold fibrations and multinets on the corresponding matroid. Another tool is a polarization construction, based on the parallel connection operad for matroids. Our main result gives a combinatorial machine for producing arrangements whose Milnor fibers have torsion in homology.}, ID_AR = {1209.3414}, gsid = {9278734647758585811} } @misc {Suciu:ps12b, author = {Papadima, Stefan and Suciu, Alexander I}, title = {Vanishing resonance and representations of {L}ie algebras}, MRCLASS = {17B10, 20J05 (20E36, 57M07)}, keywords = {{K}oszul module, resonance variety, root system, weights, {A}lexander invariant, {T}orelli group}, abstract = {We explore a relationship between the classical representation theory of a complex, semisimple Lie algebra $\mathfrak{g}$ and the resonance varieties $\mathcal{R}(V,K)\subset V^*$ attached to irreducible $\mathfrak{g}$-modules $V$ and submodules $K\subset V\wedge V$. In the process, we give a precise roots-and-weights criterion insuring the vanishing of these varieties, or, equivalently, the finiteness of certain modules $\mathcal{W}(V,K)$ over the symmetric algebra on $V$. In the case when $\mathfrak{g}=\mathfrak{sl}_2(\mathbb{C})$, our approach sheds new light on the modules studied by {W}eyman and {E}isenbud in the context of {G}reen's conjecture on free resolutions of canonical curves. In the case when $\mathfrak{g}=\mathfrak{sl}_n(\mathbb{C})$ or $\mathfrak{sp}_{2g}(\mathbb{C})$, our approach yields a unified proof of two vanishing results for the resonance varieties of the (outer) {T}orelli groups of surface groups, results which arose in recent work by {D}imca, {H}ain, and the authors on homological finiteness in the {J}ohnson filtration of mapping class groups and automorphism groups of free groups.}, ID_AR = {1207.2038}, gsid = {7778481324580566017} } @misc {Suciu:syz12, author = {Suciu, Alexander I. and Yang, Yaping and Zhao, Gufang}, title = {Homological finiteness of abelian covers}, JOURNAL = {Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)}, FJOURNAL = {Annali della Scuola Normale Superiore di Pisa}, YEAR = {}, month = {}, Number = {}, Pages = {}, MRCLASS = {14F35, 55N25 (20J05, 57M07)}, MRNUMBER = {}, MRREVIEWER = {}, ZBLNUMBER = {}, ZBREVIEWER = {}, keywords = {Abelian cover, characteristic variety, {D}wyer--{F}ried set, {G}rassmannian}, abstract = {We present a method for deciding when a regular abelian cover of a finite CW-complex has finite Betti numbers. To start with, we describe a natural parameter space for all regular covers of a finite CW-complex $X$, with group of deck transformations a fixed abelian group $A$, which in the case of free abelian covers of rank $r$ coincides with the Grassmanian of $r$-planes in $H^1(X,\Q)$. Inside this parameter space, there is a subset $\Omega_A^i(X)$ consisting of all the covers with finite Betti numbers up to degree $i$. Building up on work of Dwyer and Fried, we show how to compute these sets in terms of the jump loci for homology with coefficients in rank~$1$ local systems on $X$. For certain spaces, such as smooth, quasi-projective varieties, the generalized Dwyer--Fried invariants that we introduce here can be computed in terms of intersections of algebraic subtori in the character group. For many spaces of interest, the homological finiteness of abelian covers can be tested through the corresponding free abelian covers. Yet in general, abelian covers exhibit different homological finiteness properties than their free abelian counterparts.}, doi = {10.2422/2036-2145.201205_008}, ID_AR = {1204.4873}, gsid = {4301353495952639806} } @article {Suciu:ais13, author = {Suciu, Alexander I.}, title = {Characteristic varieties and {B}etti numbers of free abelian covers}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2013}, month = {}, Number = {}, Pages = {62 pages}, MRCLASS = {14F35, 55N25 (20J05, 32S22, 57M07, 57M12)}, MRNUMBER = {}, MRREVIEWER = {}, ZBLNUMBER = {}, ZBREVIEWER = {}, keywords = {Free abelian cover, characteristic variety, exponential tangent cone, {D}wyer--{F}ried set, special {S}chubert variety, translated subtorus, {K}{\"{a}}hler manifold, quasi-{K}{\"{a}}hler manifold, hyperplane arrangement, property ${\rm FP}_n$.}, abstract = {The regular $\Z^r$-covers of a finite cell complex $X$ are parameterized by the Grassmannian of $r$-planes in $H^1(X,\Q)$. Moving about this variety, and recording when the Betti numbers $b_1,\dots, b_i$ of the corresponding covers are finite carves out certain subsets $\Omega^i_r(X)$ of the Grassmannian. We present here a method, essentially going back to Dwyer and Fried, for computing these sets in terms of the jump loci for homology with coefficients in rank~$1$ local systems on $X$. Using the exponential tangent cones to these jump loci, we show that each $\Omega$-invariant is contained in the complement of a union of Schubert varieties associated to an arrangement of linear subspaces in $H^1(X,\Q)$. The theory can be made very explicit in the case when the characteristic varieties of $X$ are unions of translated tori. But even in this setting, the $\Omega$-invariants are not necessarily open, not even when $X$ is a smooth complex projective variety. As an application, we discuss the geometric finiteness properties of some classes of groups.}, ID_AR = {1111.5803}, gsid = {4037310650460849423}, doi = {10.1093/imrn/rns246} } @article{Suciu:syz13, author = {Suciu, Alexander I. and Yang, Yaping and Zhao, Gufang}, title = {Intersections of translated algebraic subtori}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {217}, YEAR = {2013}, NUMBER = {3}, PAGES = {481-494}, MRCLASS = {20G20 (18B35, 20E15, 55N25)}, MRNUMBER = {2974227}, MRREVIEWER = {}, ZBLNUMBER = {}, ZBREVIEWER = {}, keywords = {Complex algebraic torus, {P}ontrjagin duality, lattice of subgroups, primitive subgroup, translated algebraic subgroup, determinant group, characteristic variety, fibered category}, abstract = {We exploit the classical correspondence between finitely generated abelian groups and abelian complex algebraic reductive groups to study the intersection theory of translated subgroups in an abelian complex algebraic reductive group, with special emphasis on intersections of (torsion) translated subtori in an algebraic torus.}, ID_AR = {1109.1023}, gsid = {10943220494671999175}, DOI = {10.1016/j.jpaa.2012.06.025} } @incollection {Suciu:ais12b, author = {Suciu, Alexander I.}, title = {Geometric and homological finiteness in free abelian covers}, SERIES = {Publications of the Scuola Normale Superiore, CRM Series}, FSERIES = {}, BOOKTITLE = {Configuration Spaces: Geometry, Topology and Combinatorics}, VOLUME = {14}, PAGES = {461--501}, PUBLISHER = {Edizioni della Normale}, ADDRESS = {Pisa}, YEAR = {2012}, ISBN = {978-8876424304}, EDITOR = {Anders Bj{\"{o}}rner, Fred Cohen, Corrado De Concini, Claudo Procesi, Mario Salvetti}, MRCLASS = {20J05 (20F36, 32S22, 55N25, 57M07)}, MRNUMBER = {}, MRREVIEWER = {}, ZBLNUMBER = {}, ZBREVIEWER = {}, keywords = {{B}ieri--{N}eumann--{S}trebel--{R}enz invariant, free abelian cover, {D}wyer--{F}ried invariant, characteristic variety, exponential tangent cone, resonance variety, toric complex, quasi-projective variety, configuration space, hyperplane arrangement}, abstract = {We describe some of the connections between the {B}ieri--{N}eumann--{S}trebel--{R}enz invariants, the {D}wyer--{F}ried invariants, and the cohomology support loci of a space $X$. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of $X$ can be expressed in terms of the resonance varieties, extracted from the cohomology ring of $X$. In general, though, translated components in the characteristic varieties affect the answer. We illustrate this theory in the setting of toric complexes, as well as smooth, complex projective and quasi-projective varieties, with special emphasis on configuration spaces of {R}iemann surfaces, and complements of hyperplane arrangements.}, ID_AR = {1112.0948}, gsid = {8933560789269450749} } @article {Suciu:ps12a, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Homological finiteness in the {J}ohnson filtration of the automorphism group of a free group}, JOURNAL = {J. Topol.}, FJOURNAL = {Journal of Topology}, VOLUME = {5}, YEAR = {2012}, NUMBER = {4}, PAGES = {909-944}, MRCLASS = {20E36, 20J05 (20F14, 20G05, 55N25)}, MRNUMBER = {}, MRREVIEWER = {}, ZBLNUMBER = {}, ZBREVIEWER = {}, keywords = {Automorphism group of free group, {T}orelli group, {J}ohnson filtration, {J}ohnson homomorphism, resonance variety, characteristic variety, {A}lexander invariant}, abstract = {We examine the {J}ohnson filtration of the (outer) automorphism group of a finitely generated group. In the case of a free group, we find a surprising result: the first {B}etti number of the second subgroup in the {J}ohnson filtration is finite. Moreover, the corresponding {A}lexander invariant is a non-trivial module over the Laurent polynomial ring. In the process, we show that the first resonance variety of the outer {T}orelli group of a free group is trivial. We also establish a general relationship between the {A}lexander invariant and its infinitesimal counterpart.}, ID_AR = {1011.5292}, url = {http://jtopol.oxfordjournals.org/content/early/2012/09/19/jtopol.jts023.abstract}, gsid = {759587536925193451}, doi = {10.1112/jtopol/jts023} } @incollection {Suciu:ais12a, author = {Suciu, Alexander I.}, title = {Resonance varieties and {D}wyer-{F}ried invariants}, SERIES = {Adv. Stud. Pure Math.}, FSERIES = {Advanced Studies in Pure Mathematics}, BOOKTITLE = {Arrangements of Hyperplanes---Sapporo 2009}, VOLUME = {62}, PAGES = {359-398}, PUBLISHER = {Kinokuniya}, ADDRESS = {Tokyo}, YEAR = {2012}, ISBN = {9784931469679}, EDITOR = {Hiroaki Terao and Sergey Yuzvinsky}, MRCLASS = {20J05, 55N25 (14F35, 32S22, 55R80, 57M07)}, MRNUMBER = {2933803}, MRREVIEWER = {}, ZBLNUMBER = {06077484}, ZBREVIEWER = {}, keywords = {Free abelian cover, characteristic variety, resonance variety, tangent cone, {D}wyer--{F}ried set, special {S}chubert variety, toric complex, {K}{\"{a}}hler manifold, hyperplane arrangement}, abstract = {The {D}wyer--{F}ried invariants of a finite cell complex $X$ are the subsets $\Omega^i_r(X)$ of the {G}rassmannian of $r$-planes in $H^1(X,\Q)$ which parametrize the regular $\Z^r$-covers of $X$ having finite {B}etti numbers up to degree~$i$. In previous work, we showed that each $\Omega$-invariant is contained in the complement of a union of {S}chubert varieties associated to a certain subspace arrangement in $H^1(X,\Q)$. Here, we identify a class of spaces for which this inclusion holds as equality. For such ``straight" spaces $X$, all the data required to compute the $\Omega$-invariants can be extracted from the resonance varieties associated to the cohomology ring $H^*(X,\Q)$. In general, though, translated components in the characteristic varieties affect the answer.}, ID_AR = {1111.4534}, gsid = {13261373504940347779} } @article {Suciu:mz11, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, title = {Quasi-{K}{\"{a}}hler groups, 3-manifold groups, and formality}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {268}, YEAR = {2011}, NUMBER = {1}, PAGES = {169--186}, MRCLASS = {14F35, 20F34, 57N10 (55N25, 55P62)}, MRNUMBER = {2805428}, MRREVIEWER = {Andrzej Kozlowski}, ZBLNUMBER = {1228.14018}, ZBREVIEWER = {Aleksandr G. Aleksandrov}, keywords = {Quasi-{K}{\"{a}}hler manifold, $3$-manifold, cut number, isolated surface singularity, $1$-formal group, cohomology ring, characteristic variety, resonance variety}, abstract = {In this note, we address the following question: Which $1$-formal groups occur as fundamental groups of both quasi-{K}{\"{a}}hler manifolds and closed, connected, orientable $3$-manifolds. We classify all such groups, at the level of {M}alcev completions, and compute their coranks. Dropping the assumption on realizability by $3$-manifolds, we show that the corank equals the isotropy index of the cup-product map in degree one. Finally, we examine the formality properties of smooth affine surfaces and quasi-homogeneous isolated surface singularities. In the latter case, we describe explicitly the positive-dimensional components of the first characteristic variety for the associated singularity link.}, ID_AR = {0810.2158}, URL = {http://www.springerlink.com/content/q475773366186q08/}, DOI = {10.1007/s00209-010-0664-y} } @incollection {Suciu:conm11, author = {Suciu, Alexander I.}, title = {Fundamental groups, {A}lexander invariants, and cohomology jumping loci}, BOOKTITLE = {Topology of algebraic varieties and singularities}, SERIES = {Contemp. Math.}, FSERIES = {Contemporary Mathematics}, VOLUME = {538}, PAGES = {179--223}, EDITOR = {Jos\'{e} Ignacio Cogolludo-Agust\'{\i}n and Eriko Hironaka}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2011}, MRCLASS = {20F34 (20J05, 32S22, 57M12)}, MRNUMBER = {2777821 (2012b:20092)}, MRREVIEWER = {F. E. A. Johnson}, ZBLNUMBER = {1214.14017}, ZBREVIEWER = {}, keywords = {Fundamental group, {A}lexander polynomial, characteristic variety, resonance variety, abelian cover, formality, {B}ieri--{N}eumann--{S}trebel--{R}enz invariant, right-angled {A}rtin group, {K}{\"{a}}hler manifold, quasi-{K}{\"{a}}hler manifold, hyperplane arrangement, {M}ilnor fibration, boundary manifold}, abstract = {We survey the cohomology jumping loci and the {A}lexander-type invariants associated to a space, or to its fundamental group. Though most of the material is expository, we provide new examples and applications, which in turn raise several questions and conjectures. The jump loci of a space $X$ come in two basic flavors: the characteristic varieties, or, the support loci for homology with coefficients in rank $1$ local systems, and the resonance varieties, or, the support loci for the homology of the cochain complexes arising from multiplication by degree $1$ classes in the cohomology ring of $X$. The geometry of these varieties is intimately related to the formality, (quasi-) projectivity, and homological finiteness properties of $\pi_1(X)$. We illustrate this approach with various applications to the study of hyperplane arrangements, Milnor fibrations, $3$-manifolds, and right-angled Artin groups.}, ID_AR = {0910.1559}, URL = {http://www.math.neu.edu/~suciu/papers/libsurvey.pdf}, gsid = {11027901707018836620}, DOI = {10.1090/conm/538} } @article {Suciu:forum10, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Algebraic monodromy and obstructions to formality}, JOURNAL = {Forum Math.}, FJOURNAL = {Forum Mathematicum}, VOLUME = {22}, YEAR = {2010}, NUMBER = {5}, PAGES = {973-983}, MRCLASS = {20J05, 57M07 (20F34, 55P62)}, MRNUMBER = {2719766 (2011j:57004)}, MRREVIEWER = {Masaki Kameko}, ZBLNUMBER = {1229.57002}, ZBREVIEWER = {Samuel Smith}, keywords = {Fibration, monodromy, formality, cohomology jumping loci, link, singularity}, abstract = {Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more general result about iterated group extensions. As an application, we obtain new criteria for formality of spaces, and 1-formality of groups, illustrated by bundle constructions and various examples from low-dimensional topology and singularity theory.}, ID_AR = {0901.0105}, URL = {http://www.reference-global.com/doi/abs/10.1515/FORUM.2010.052}, gsid = {9921396940464328718}, DOI = {10.1515/forum.2010.052}} @article {Suciu:plms10, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Bieri-{N}eumann-{S}trebel-{R}enz invariants and homology jumping loci}, JOURNAL = {Proc. London Math. Soc.}, FJOURNAL = {Proceedings of the London Mathematical Society}, VOLUME = {100}, YEAR = {2010}, NUMBER = {3}, PAGES = {795-834}, MRCLASS = {20J05 (55N25, 14F35, 20F36, 20F65)}, MRNUMBER = {MR2640291 (2011i:55006)}, MRREVIEWER = {Brita E. A. Nucinkis}, ZBLNUMBER = {05708721}, ZBREVIEWER = {}, keywords = {Characteristic variety, {A}lexander variety, resonance variety, exponential tangent cone, homology of free abelian covers, {B}ieri-{N}eumann-{S}trebel-{R}enz invariant, {N}ovikov homology, valuation, algebraic integer, right-angled {A}rtin group, {A}rtin kernel, {K}{\"{a}}hler manifold, quasi-{K}{\"{a}}hler manifold}, abstract = {We investigate the relationship between the geometric {B}ieri-{N}eumann-{S}trebel-{R}enz invariants of a space (or of a group) and the jump loci for homology with coefficients in rank-$1$ local systems over a field. We give computable upper bounds for the geometric invariants in terms of the exponential tangent cones to the jump loci over the complex numbers. Under suitable hypotheses, these bounds can be expressed in terms of simpler data, for instance, the resonance varieties associated to the cohomology ring. These techniques yield information on the homological finiteness properties of free abelian covers of a given space and of normal subgroups with abelian quotients of a given group. We illustrate our results in a variety of geometric and topological contexts, such as toric complexes and {A}rtin kernels, as well as {K}{\"{a}}hler and quasi-{K}{\"{a}}hler manifolds.}, ID_AR = {0812.2660}, URL = {http://plms.oxfordjournals.org/cgi/content/abstract/pdp045}, gsid = {14133650059252773982}, DOI = {10.1112/plms/pdp045} } @article {Suciu:tams10, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {The spectral sequence of an equivariant chain complex and homology with local coefficients}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {362}, YEAR = {2010}, NUMBER = {5}, PAGES = {2685-2721}, MRCLASS = {55T99 (20J05, 55N25, 57M05)}, MRNUMBER = {2584616 (2011b:55017)}, MRREVIEWER = {Masaki Kameko}, ZBLNUMBER = {1195.55005}, ZBREVIEWER = {Haruo Minami}, keywords = {Equivariant chain complex, $I$-adic filtration, spectral sequence, twisted homology, minimal cell complex, {A}omoto complex, {B}etti numbers}, abstract = {We study the spectral sequence associated to the filtration by powers of the augmentation ideal on the (twisted) equivariant chain complex of the universal cover of a connected CW-complex $X$. In the process, we identify the $d^1$ differential in terms of the coalgebra structure of $H_*(X,\k)$, and the $\k\pi_1(X)$-module structure on the twisting coefficients. In particular, this recovers in dual form a result of Reznikov, on the mod $p$ cohomology of cyclic $p$-covers of aspherical complexes. This approach provides information on the homology of all {G}alois covers of $X$. It also yields computable upper bounds on the ranks of the cohomology groups of $X$, with coefficients in a prime-power order, rank one local system. When $X$ admits a minimal cell decomposition, we relate the linearization of the equivariant cochain complex of the universal abelian cover to the {A}omoto complex, arising from the cup-product structure of $H^*(X,\k)$, thereby generalizing a result of {C}ohen and {O}rlik.}, ID_AR = {0706.4262}, URL = {http://www.ams.org/tran/2010-362-05/S0002-9947-09-05041-7/}, DOI = {10.1090/S0002-9947-09-05041-7} } @book {Suciu:alss10, TITLE = {Arrangements, local systems and singularities}, EDITOR = {El Zein, Fouad and Suciu, Alexander I. and Tosun, Meral and Uluda{\u{g}}, A. Muhammed and Yuzvinsky, Sergey}, NOTE = {Lecture notes from the CIMPA Summer School held at Galatasaray University, Istanbul, June 11-22, 2007}, PUBLISHER = {Birk{\"{a}}user}, ADDRESS = {Basel, Boston, Berlin}, SERIES = {Progress in Mathematics}, YEAR = {2010}, PAGES = {i-x and 1-319}, ISBN = {978-3-0346-0208-2}, MRCLASS = {}, MRNUMBER = {}, ZBLNUMBER = {}, DOI = {10.1007/978-3-0346-0209-9}, URL = {http://www.springerlink.com/content/978-3-0346-0208-2} } @article {Suciu:bmssmr09, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Geometric and algebraic aspects of $1$-formality}, JOURNAL = {Bull. Math. Soc. Sci. Math. Roumanie (N.S.)}, FJOURNAL = {Bulletin Math\'ematique de la Soci\'et\'e des Sciences Math\'ematiques de Roumanie. Nouvelle S\'erie}, VOLUME = {52 (100)}, YEAR = {2009}, NUMBER = {3}, PAGES = {355-375}, MRCLASS = {55P62 (57M07, 14F35, 20J05, 55N25)}, MRNUMBER = {2554494 (2010k:55018)}, MRREVIEWER = {John F. Oprea}, ZBLNUMBER = {1199.55010 }, ZBREVIEWER = {Corina Mohorianu}, Keywords = {Formality, fundamental group, cohomology jumping loci, holonomy {L}ie algebra, {B}ieri--{N}eumann--{S}trebel invariant, {M}alcev completion, lower central series, {K}{\"{a}}hler manifold, quasi-{K}{\"{a}}hler manifold, {M}ilnor fiber, hyperplane arrangement, {A}rtin group, {B}estvina--{B}rady group, pencil, fibration, monodromy}, abstract = {Formality is a topological property, defined in terms of {S}ullivan's model for a space. In the simply-connected setting, a space is formal if its rational homotopy type is determined by the rational cohomology ring. In the general setting, the weaker $1$-formality property allows one to reconstruct the rational pro-unipotent completion of the fundamental group, solely from the cup products of degree $1$ cohomology classes. In this note, we survey various facets of formality, with emphasis on the geometric and algebraic implications of $1$-formality, and its relations to the cohomology jump loci and the {B}ieri--{N}eumann--{S}trebel invariant. We also produce examples of $4$-manifolds $W$ such that, for every compact {K}{\"{a}}hler manifold $M$, the product $M\times W$ has the rational homotopy type of a {K}{\"{a}}hler manifold, yet $M\times W$ admits no {K}{\"{a}}hler metric.}, URL = {http://www.rms.unibuc.ro/bulletin/volumes/52-3/node16.html}, ID_AR = {0903.2307} } @article {Suciu:duke09, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, title = {Topology and geometry of cohomology jump loci}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {148}, YEAR = {2009}, NUMBER = {3}, PAGES = {405-457}, MRCLASS = {14F35 (20F14, 55N25, 14M12, 20F36, 55P62)}, MRNUMBER = {2527322 (2011b:14047)}, MRREVIEWER = {}, ZBLNUMBER = {1222.14035}, ZBREVIEWER = {Keith Johnson}, keywords = {Characteristic variety, resonance variety, $1$-formal group, holonomy {L}ie algebra, {M}alcev completion, {A}lexander invariant, tangent cone, smooth quasi-projective variety, arrangement, configuration space, {A}rtin group}, abstract = {We elucidate the key role played by formality in the theory of characteristic and resonance varieties. We define relative characteristic and resonance varieties, $V_k$ and $R_k$, related to twisted group cohomology with coefficients of arbitrary rank. We show that the germs at the origin of $V_k$ and $R_k$ are analytically isomorphic if the group is $1$-formal; in particular, the tangent cone to $V_k$ at $1$ equals $R_k$. These new obstructions to $1$-formality lead to a striking rationality property of the usual resonance varieties. A detailed analysis of the irreducible components of the tangent cone at $1$ to the first characteristic variety yields powerful obstructions to realizing a finitely presented group as the fundamental group of a smooth, complex quasi-projective algebraic variety. This sheds new light on a classical problem of {J}.-{P}. {S}erre. Applications to arrangements, configuration spaces, coproducts of groups, and {A}rtin groups are given.}, ID_AR = {0902.1250}, URL = {http://projecteuclid.org/euclid.dmj/1245350753}, DOI = {10.1215/00127094-2009-030} } @article {Suciu:jems09, author = {Dimca, Alexandru and Suciu, Alexander I.}, title = {Which 3-manifold groups are {K}{\"{a}}hler groups?}, JOURNAL = {J. Eur. Math. Soc. (JEMS)}, FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, VOLUME = {11}, YEAR = {2009}, NUMBER = {3}, PAGES = {521-528}, MRCLASS = {20F34 (32J27, 57N10)}, MRNUMBER = {2505439 (2011f:32041)}, MRREVIEWER = {}, ZBLNUMBER = {1217.57011}, ZBREVIEWER = {Qilin Yang}, keywords = {{K}{\"{a}}hler manifold, $3$-manifold, fundamental group, cohomology ring, resonance variety, isotropic subspace}, abstract = {The question in the title, first raised by {G}oldman and {D}onaldson, was partially answered by {R}eznikov. We give a complete answer, as follows: if $G$ can be realized as both the fundamental group of a closed $3$-manifold and of a compact {K}{\"{a}}hler manifold, then $G$ must be finite, and thus belongs to the well-known list of finite subgroups of ${\rm O}(4)$, acting freely on $S^3$.}, ID_AR = {0709.4350}, URL = {http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=11&iss=3&rank=3}, DOI = {10.4171/JEMS/158} } @article {Suciu:crelle09, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, title = {Non-finiteness properties of fundamental groups of smooth projective varieties}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f{\"u}r die Reine und Angewandte Mathematik [Crelle's Journal]}, VOLUME = {629}, YEAR = {2009}, NUMBER = {}, PAGES = {89-105}, MRCLASS = {14F35 (57M07, 14H30, 20J05)}, MRNUMBER = {2527414}, MRREVIEWER = {}, ZBLNUMBER = {1170.14017}, ZBREVIEWER = {Roberto Pignatelli}, abstract = {For each integer $n>1$, we construct an irreducible, smooth, complex projective variety $M$ of dimension $n$, whose fundamental group has infinitely generated homology in degree $n+1$ and whose universal cover is a {S}tein manifold, homotopy equivalent to an infinite bouquet of $n$-dimensional spheres. This non-finiteness phenomenon is also reflected in the fact that the homotopy group $pi_n(M)$, viewed as a module over $\matbbb{Z}\pi_1(M)$, is free of infinite rank. As a result, we give a negative answer to a question of {K}oll{\'a}r on the existence of quasi-projective classifying spaces (up to commensurability) for the fundamental groups of smooth projective varieties. To obtain our examples, we develop a complex analog of a method in geometric group theory due to {B}estvina and {B}rady.}, ID_AR = {math.AG/0609456}, URL = {http://www.reference-global.com/doi/abs/10.1515/CRELLE.2009.027}, DOI = {10.1515/crelle.2009.027} } @article {Suciu:adv09, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Toric complexes and {A}rtin kernels}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {220}, YEAR = {2009}, month = {jan}, NUMBER = {2}, PAGES = {441-477}, MRCLASS = {57M07 (20F36 55N25 55P62)}, MRNUMBER = {2466422 (2010h:57007)}, MRREVIEWER = {Michael J. Falk}, ZBLNUMBER = {1208.57002}, ZBREVIEWER = {Michael J. Falk}, Keywords = {toric complex, right-angled {A}rtin group, {A}rtin kernel, {B}estvina-{B}rady group, cohomology ring, {S}tanley-{R}eisner ring, cohomology jumping loci, monodromy action, holonomy {L}ie algebra, {M}alcev {L}ie algebra, formality}, abstract = {A simplicial complex $L$ on $n$ vertices determines a subcomplex $T_L$ of the $n$-torus, with fundamental group the right-angled {A}rtin group $G_{L}$. Given an epimorphism $\chi\colon G_{L}\to \Z$, let $T_L^{\chi}$ be the corresponding cover, with fundamental group the {A}rtin kernel $N_{\chi}$. We compute the cohomology jumping loci of the toric complex $T_L$, as well as the homology groups of $T_L^{\chi}$ with coefficients in a field $\k$, viewed as modules over the group algebra $\k\Z$. We give combinatorial conditions for $H_{\le r}(T_L^{\chi};\k)$ to have trivial $\Z$-action, allowing us to compute the truncated cohomology ring, $H^{\le r}(T_L^{\chi};\k)$. We also determine several {L}ie algebras associated to {A}rtin kernels, under certain triviality assumptions on the monodromy $\Z$-action, and establish the $1$-formality of these (not necessarily finitely presentable) groups.}, ID_AR = {0801.3626}, % URL = {http://www.math.neu.edu/~suciu/papers/toric.pdf}, DOI = {10.1016/j.aim.2008.09.008} } @incollection {Suciu:gtm08, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {The boundary manifold of a complex line arrangement}, BOOKTITLE = {Groups, homotopy and configuration spaces}, SERIES = {Geom. Topol. Monogr.}, YEAR = {2008}, month = {}, VOLUME = {13}, PAGES = {105-146}, PUBLISHER = {Geom. Topol. Publ., Coventry}, MRCLASS = {32S22, 57M27}, MRNUMBER = {2508203 (2010c:32051)}, MRREVIEWER = {Henry K. Schenck}, ZBLNUMBER = {1137.32013}, ZBREVIEWER = {}, keywords = {line arrangement, graph manifold, fundamental group, twisted {A}lexander polynomial, {BNS} invariant, cohomology ring, holonomy {L}ie algebra, characteristic variety, resonance variety, tangent cone, formality}, abstract = {We study the topology of the boundary manifold of a line arrangement in $\mathbb{CP}^2$, with emphasis on the fundamental group $G$ and associated invariants. We determine the {A}lexander polynomial $\Delta(G)$, and more generally, the twisted {A}lexander polynomial associated to the abelianization of $G$ and an arbitrary complex representation. We give an explicit description of the unit ball in the {A}lexander norm, and use it to analyze certain {B}ieri–-{N}eumann-–{S}trebel invariants of $G$. From the {A}lexander polynomial, we also obtain a complete description of the first characteristic variety of $G$. Comparing this with the corresponding resonance variety of the cohomology ring of $G$ enables us to characterize those arrangements for which the boundary manifold is formal.}, ID_AR = {math.GT/0607274}, URL = {http://www.msp.warwick.ac.uk/gtm/2008/13/p005.xhtml}, DOI = {10.2140/gtm.2008.13.105} } @article {Suciu:imrn08, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, title = {Alexander polynomials: Essential variables and multiplicities}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2008}, month = {}, Number = {3}, Pages = {Art. ID rnm119, 36 pp.}, MRCLASS = {32S22 (20F65 55R80 57M27)}, MRNUMBER = {2416998 (2009i:32036)}, MRREVIEWER = {Michael J. Falk}, ZBLNUMBER = {1156.32018}, ZBREVIEWER = {Claus Ernst}, keywords = {characteristic varieties, {A}lexander polynomial, almost principal ideal, multiplicity, twisted {B}etti number, quasi-projective group, boundary manifold, {S}eifert link}, abstract = {We explore the codimension-one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable {A}lexander polynomial. As an application, we give new criteria that must be satisfied by fundamental groups of smooth, quasi-projective complex varieties. These criteria establish precisely which fundamental groups of boundary manifolds of complex line arrangements are quasi-projective. We also give sharp upper bounds for the twisted {B}etti ranks of a group, in terms of multiplicities constructed from the {A}lexander polynomial. For {S}eifert links in homology $3$-spheres, these bounds become equalities, and our formula shows explicitly how the {A}lexander polynomial determines all the characteristic varieties.}, ID_AR = {0706.2499}, URL = {http://imrn.oxfordjournals.org/cgi/content/abstract/2008/rnm119/rnm119}, DOI = {10.1093/imrn/rnm119} } @article {Suciu:jag08, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, title = {Quasi-{K}{\"{a}}hler {B}estvina-{B}rady groups}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {17}, YEAR = {2008}, month = {}, NUMBER = {1}, PAGES = {185-197}, MRCLASS = {20F65, 14F35}, MRNUMBER = {2357684 (2008i:20052)}, MRREVIEWER = {Eddy Godelle}, ZBLNUMBER = {1176.20037}, ZBREVIEWER = {}, keywords = {fundamental groups, quasi-{K}{\"{a}}hler groups, compact {K}{\"{a}}hler manifolds, finite simple graphs, right-angled {A}rtin groups, {B}estvina-{B}rady groups, resonance varieties}, abstract = {A finite simple graph $\Gamma$ determines a right-angled {A}rtin group $G_{\Gamma}$, with one generator for each vertex $v$, and with one commutator relation $vw=wv$ for each pair of vertices joined by an edge. The {B}estvina-{B}rady group $N_{\Gamma}$ is the kernel of the projection $G_{\Gamma} \to \mathbb{Z}$, which sends each generator $v$ to $1$. We establish precisely which graphs $\Gamma$ give rise to quasi-{K}{\"{a}}ahler (respectively, {K}{\"{a}}ahler) groups $N_{\Gamma}$. This yields examples of quasi-projective groups which are not commensurable (up to finite kernels) to the fundamental group of any aspherical, quasi-projective variety.}, ID_AR = {math.AG/0603446}, URL = {http://www.ams.org/distribution/jag/2008-17-01/S1056-3911-07-00463-8/home.html} } @article {Suciu:mathann08, AUTHOR = {Kreck, Matthias and Suciu, Alexander I.}, TITLE = {Free abelian covers, short loops, stable length, and systolic inequalities}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {340}, YEAR = {2008}, month = {}, NUMBER = {3}, PAGES = {709--729}, % note = {initial preprint together with Katz, Mikhail G.}, MRCLASS = {53C23 (57N65)}, MRNUMBER = {2358001 (2008k:53079)}, MRREVIEWER = {Florent Balacheff}, ZBLNUMBER = {1134.53019}, ZBREVIEWER = {Mircea Craioveanu}, keywords = {}, abstract = {We explore the geometry of the {A}bel-{J}acobi map $f$ from a closed, orientable Riemannian manifold $X$ to its {J}acobi torus. Applying {G}romov's filling inequality to the typical fiber of $f$, we prove an interpolating inequality for two flavors of shortest length invariants of loops. The procedure works, provided the lift of the fiber is non-trivial in the homology of the maximal free abelian cover, $\tilde{X}$, classified by $f$. We show that the finite-dimensionality of the rational homology of $\tilde{X}$ is a sufficient condition for the homological non-triviality of the fiber. When applied to nilmanifolds, our ``fiberwise'' inequality typically gives stronger information than the filling inequality for $X$ itself. In dimension $3$, we present a sufficient non-vanishing condition in terms of {M}assey products. This condition holds for certain manifolds that do not fiber over their {J}acobi torus, such as $0$-framed surgeries on suitable links. Our systolic inequality applies to surface bundles over the circle (provided the algebraic monodromy has $1$-dimensional coinvariants), even though the {M}assey product invariant vanishes for some of these bundles.}, ID_AR = {math.DG/0207143v1}, URL = {http://www.springerlink.com/content/c2732614k8626687}, DOI = {10.1007/s00208-007-0182-3} } @article {Suciu:jlms07, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Algebraic invariants for {B}estvina-{B}rady groups}, JOURNAL = {J. London Math. Soc.}, FJOURNAL = {Journal of the London Mathematical Society}, VOLUME = {76}, YEAR = {2007}, month = {}, NUMBER = {2}, PAGES = {273-292}, MRCLASS = {20F36 (20F14 57M07 57M27)}, MRNUMBER = {2363416}, MRREVIEWER = {}, ZBLNUMBER = {1176.20037}, ZBREVIEWER = {}, keywords = {Graph, flag complex, right-angled {A}rtin group, {B}estvina--{B}rady group, lower central series, holonomy {L}ie algebra, {C}hen {L}ie algebra, resonance variety, {A}lexander invariant}, abstract = {{B}estvina--{B}rady groups arise as kernels of length homomorphisms from right-angled {A}rtin groups $G_\Gamma$ to the integers. Under some connectivity assumptions on the flag complex $\Delta_\Gamma$, we compute several algebraic invariants of such a group $N_\Gamma$, directly from the underlying graph $\Gamma$. As an application, we give examples of {B}estvina--{B}rady groups which are not isomorphic to any {A}rtin group or arrangement group.}, ID_AR = {math.GR/0603240}, URL = {http://jlms.oxfordjournals.org/cgi/content/abstract/jdm045}, DOI = {10.1112/jlms/jdm045} } @article {Suciu:pamq07, author = {Denham, Graham and Suciu, Alexander I.}, title = {Moment angle complexes, monomial ideals, and {M}assey products}, JOURNAL = {Pure Appl. Math. Q.}, FJOURNAL = {Pure and Applied Mathematics Quarterly}, VOLUME = {3}, YEAR = {2007}, month = {}, NUMBER = {1}, PAGES = {25-60}, MRCLASS = {55S30 (13F55, 16E05, 32Q55, 55P62, 57R19)}, MRNUMBER = {2330154 (2008g:55028)}, MRREVIEWER = {Marc Aubry}, ZBLNUMBER = {1169.13013}, ZBREVIEWER = {{M}artin D. Crossley}, KEYWORDS = {Moment-angle complex, cohomology ring, homotopy {L}ie algebra, {S}tanley-{R}eisner ring, {E}ilenberg-{M}oore spectral sequence, cellular cochain algebra, formality, {M}assey product, triangulation, {B}ier sphere, subspace arrangement, complex manifold}, abstract = {Associated to every finite simplicial complex $K$ there is a ``moment-angle" finite {CW}-complex, ${\mathcal{Z}}_{K}$; if $K$ is a triangulation of a sphere, ${\mathcal{Z}}_{K}$ is a smooth, compact manifold. Building on work of {B}uchstaber, {P}anov, and {B}askakov, we study the cohomology ring, the homotopy groups, and the triple {M}assey products of a moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given.}, ID_AR = {math.AT/0512497}, URL = {http://www.intlpress.com/JPAMQ/p/2007/25-60.pdf}, URL = {http://pamq.henu.edu.cn/downloadarticle.jsp?id=144} } @article {Suciu:adv06, author = {Cohen, Daniel C. and Suciu, Alexander I.}, title = {Boundary manifolds of projective hypersurfaces}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {206}, YEAR = {2006}, month = {}, NUMBER = {2}, PAGES = {538-566}, MRCLASS = {14J70 (32S22 32S35)}, MRNUMBER = {2263714 (2007j:14064)}, MRREVIEWER = {Henry K. Schenck}, ZBLNUMBER = {1110.14036}, ZBREVIEWER = {Daniel Matei}, keywords = {}, abstract = {}, ID_AR = {math.AT/0502506}, DOI = {10.1016/j.aim.2005.10.003} } @article {Suciu:cmh06, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {When does the associated graded {L}ie algebra of an arrangement group decompose?}, JOURNAL = {Comment. Math. Helv.}, FJOURNAL = {Commentarii Mathematici Helvetici}, VOLUME = {81}, YEAR = {2006}, NUMBER = {4}, PAGES = {859-875}, MRNUMBER = {2271225 (2007h:52028)}, MRREVIEWER = {Ivan V. Arzhantsev}, ZBLNUMBER = {1104.52009}, ZBREVIEWER = {}, keywords = {}, abstract = {}, ID_AR = {math.CO/0309324}, URL = {http://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=81&iss=4&rank=7}, DOI = {10.4171/CMH/77} } @article {Suciu:mich06, author = {Denham, Graham and Suciu, Alexander I.}, title = {On the homotopy {L}ie algebra of an arrangement}, JOURNAL = {Michigan Math. J.}, FJOURNAL = {Michigan Mathematical Journal}, VOLUME = {54}, YEAR = {2006}, NUMBER = {2}, PAGES = {319--340}, ISSN = {0026-2285}, MRCLASS = {17B70 (16S37 17B55)}, MRNUMBER = {2252762 (2007f:17039)}, MRREVIEWER = {Marc Aubry}, ZBLNUMBER = {1198.17012}, ZBREVIEWER = {}, keywords = {Holonomy and homotopy {L}ie algebras, hyperplane arrangement, {Y}oneda algebra, {K}oszul algebra, {H}opf algebra, spectral sequence, homotopy groups}, abstract = {Let $A$ be a graded-commutative, connected $\mathbb{k}$-algebra generated in degree $1$. The homotopy {L}ie algebra $\mathfrak{g}_A$ is defined to be the {L}ie algebra of primitives of the Yoneda algebra, ${\rm Ext}_{A}(\mathbb{k},\mathbb{k})$. Under certain homological assumptions on $A$ and its quadratic closure, we express $\mathfrak{g}_A$ as a semi-direct product of the well-understood holonomy {L}ie algebra $\mathfrak{h}_A$ with a certain $\mathfrak{h}_A$-module. This allows us to compute the homotopy {L}ie algebra associated to the cohomology ring of the complement of a complex hyperplane arrangement, provided some combinatorial assumptions are satisfied. As an application, we give examples of hyperplane arrangements whose complements have the same Poincar{\'{e}} polynomial, the same fundamental group, and the same holonomy {L}ie algebra, yet different homotopy {L}ie algebras.}, ID_AR = {math.AT/0502417}, URL = {http://projecteuclid.org/euclid.mmj/1156345597}, DOI = {10.1307/mmj/1156345597} } @article {Suciu:mathann06, author = {Papadima, Stefan and Suciu, Alexander I.}, title = {Algebraic invariants for right-angled {A}rtin groups}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {334}, YEAR = {2006}, NUMBER = {3}, PAGES = {533--555}, ISSN = {0025-5831}, MRCLASS = {20F36 (13F55 55P62 57M07)}, MRNUMBER = {2207874 (2006k:20078)}, MRREVIEWER = {Eddy Godelle}, ZBLNUMBER = {1165.20032}, ZBREVIEWER = {}, Keywords = {right-angled {A}rtin groups, lower central series, Chen groups, resonance varieties, finite simplicial graphs, hyperplane arrangements}, abstract = {}, ID_AR = {math.GR/0412520}, URL = {http://www.springerlink.com/content/fx2681l300513430}, DOI = {10.1007/s00208-005-0704-9} } @article {Suciu:tams06, author = {Schenck, Henry K. and Suciu, Alexander I.}, title = {Resonance, linear syzygies, {C}hen groups, and the {B}ernstein-{G}elfand-{G}elfand correspondence}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {358}, YEAR = {2006}, NUMBER = {5}, PAGES = {2269--2289}, ISSN = {0002-9947}, MRCLASS = {52C35 (16E05)}, MRNUMBER = {2197444 (2007a:52026)}, MRREVIEWER = {Hiroaki Terao}, ZBLNUMBER = {1153.52008}, ZBREVIEWER = {}, keywords = {}, abstract = {}, ID_AR = {math.AC/0502438}, URL = {http://www.ams.org/tran/2006-358-05/S0002-9947-05-03853-5}, DOI = {10.1090/S0002-9947-05-03853-5} } @unpublished {Suciu:dps05, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, title = {Formality, {A}lexander invariants, and a question of {S}erre}, note = {preprint, December 2005 (updated December 2007)}, ID_AR = {math.AT/0512480}, URL = {http://www.math.neu.edu/~suciu/papers/serre.pdf} } @incollection {Suciu:emissary05, AUTHOR = {Falk, Michael J. and Suciu, Alexander I.}, TITLE = {Complex hyperplane arrangements}, BOOKTITLE = {Emissary (MSRI Newsletter)}, VOLUME = {Spring}, PAGES = {4--6}, PUBLISHER = {Mathematical Sciences Research Institute}, ADDRESS = {Berkeley, CA}, YEAR = {2005}, keywords = {}, abstract = {}, ID_AR = {math.AG/0505166}, URL = {http://www.msri.org/ext/Emissary/EmissarySpring05.pdf} } @article {Suciu:jalg05, AUTHOR = {Matei, Daniel and Suciu, Alexander I.}, TITLE = {Counting homomorphisms onto finite solvable groups}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {286}, YEAR = {2005}, month = {apr}, NUMBER = {1}, PAGES = {161--186}, ISSN = {0021-8693}, MRCLASS = {20D10}, MRNUMBER = {2124813 (2006b:20034)}, MRREVIEWER = {Alexander Lubotsky}, ZBLNUMBER = {1116.20026}, ZBREVIEWER = {Andrea Lucchini}, keywords = {Solvable quotients, chief series, Gasch{\"{u}}tz formula, group cohomology, finite-index subgroups, Baumslag-Solitar groups, parafree groups, braid groups}, abstract = {We present a method for computing the number of epimorphisms from a finitely presented group $G$ to a finite solvable group $\G$, which generalizes a formula of Gasch{\"{u}}tz. Key to this approach are the degree $1$ and $2$ cohomology groups of $G$, with certain twisted coefficients. As an application, we count low-index subgroups of $G$. We also investigate the finite solvable quotients of the Baumslag-Solitar groups, the Baumslag parafree groups, and the {A}rtin braid groups.}, ID_AR = {math.GR/0405122}, DOI = {10.1016/j.jalgebra.2005.01.009} } @article {Suciu:gt04, AUTHOR = {Papadima, Stefan and Suciu, Alexander I.}, TITLE = {Homotopy {L}ie algebras, lower central series and the {K}oszul property}, JOURNAL = {Geom. Topol.}, FJOURNAL = {Geometry and Topology}, VOLUME = {8}, YEAR = {2004}, PAGES = {1079--1125 (electronic)}, ISSN = {1465-3060}, MRCLASS = {55Q15 (16S37 20F14 57M25 57Q45)}, MRNUMBER = {2087079 (2005g:55022)}, MRREVIEWER = {Marc Aubry}, ZBLNUMBER = {1127.55004}, ZBREVIEWER = {}, keywords = {}, abstract = {}, ID_AR = {math.AT/0110303}, URL = {http://www.msp.warwick.ac.uk/gt/2004/08/p030.xhtml}, DOI = {10.2140/gt.2004.8.1079} } @article {Suciu:imrn04, AUTHOR = {Papadima, Stefan and Suciu, Alexander I.}, TITLE = {Chen {L}ie algebras}, JOURNAL = {Int. Math. Res. Not.}, FJOURNAL = {International Mathematics Research Notices}, YEAR = {2004}, NUMBER = {21}, PAGES = {1057--1086}, ISSN = {1073-7928}, MRCLASS = {17B70 (17D10 55P62)}, MRNUMBER = {2037049 (2004m:17043)}, MRREVIEWER = {Marc Aubry}, ZBLNUMBER = {1076.17007}, ZBREVIEWER = {Daniel Tanr\'e}, keywords = {}, abstract = {}, ID_AR = {math.GR/0307087}, URL = {http://imrn.oxfordjournals.org/cgi/content/abstract/2004/21/1057}, DOI = {doi:10.1155/S1073792804132017} } @article {Suciu:agt03, AUTHOR = {Cohen, Daniel C. and Denham, Graham and Suciu, Alexander I.}, TITLE = {Torsion in {M}ilnor fiber homology}, JOURNAL = {Algebr. Geom. Topol.}, FJOURNAL = {Algebraic \& Geometric Topology}, VOLUME = {3}, YEAR = {2003}, PAGES = {511--535 (electronic)}, ISSN = {1472-2747}, MRCLASS = {32S55 (32S22 55N25)}, MRNUMBER = {1997327 (2004d:32043)}, MRREVIEWER = {Daniel Matei}, ZBLNUMBER = {1030.32022}, ZBREVIEWER = {Theo de Jong}, KEYWORDS = {}, abstract = {}, ID_AR = {math.GT/0302143}, URL = {http://www.msp.warwick.ac.uk/agt/2003/03/p016.xhtml}, DOI = {10.2140/agt.2003.3.511} } @article {Suciu:cras02, AUTHOR = {Papadima, Stefan and Suciu, Alexander I.}, TITLE = {Rational homotopy groups and {K}oszul algebras}, JOURNAL = {C. R. Math. Acad. Sci. Paris}, FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, VOLUME = {335}, YEAR = {2002}, month = {}, NUMBER = {1}, PAGES = {53--58}, ISSN = {1631-073X}, MRCLASS = {55P62}, MRNUMBER = {1920995 (2003g:55015)}, MRREVIEWER = {Octavian Cornea}, ZBLNUMBER = {1006.55007}, ZBREVIEWER = {Daniel Tanr\'e}, keywords = {homotopy groups, cohomology ring, lower central series, rescaling, Koszul algebras}, abstract = {Let $X$ and $Y$ be finite-type CW-spaces ($X$ connected, $Y$ simply connected), such that the ring $H^*(Y,\mathbb{Q})$ is a $k$-rescaling of $H^*(X,\mathbb{Q})$. If $H^*(X,\mathbb{Q})$ is a Koszul algebra, then the graded {L}ie algebra $pi_*(\Omega Y) \otimes \mathbb{Q}$ is the $k$-rescaling of $gr_*(pi_1 X) \otimes \mathbb{Q}$. If $Y$ is a formal space, then the converse holds, and $Y$ is coformal. Furthermore, if $X$ is formal, with Koszul cohomology algebra, there exist filtered group isomorphisms between the Malcev completion of $pi_1 X$, the completion of $[\Omega S^{2k+1},\Omega Y]$, and the {M}ilnor-Moore group of coalgebra maps from $H_*(\Omega S^{2k+1},\mathbb{Q})$ to $H_*(\Omega Y,\mathbb{Q})$.}, URL = {http://www.math.neu.edu/~suciu/papers/rhgka.pdf}, DOI = {10.1016/S1631-073X(02)02420-2} } @article {Suciu:tams02, AUTHOR = {Schenck, Henry K. and Suciu, Alexander I.}, TITLE = {Lower central series and free resolutions of hyperplane arrangements}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {354}, YEAR = {2002}, NUMBER = {9}, PAGES = {3409--3433 (electronic)}, ISSN = {0002-9947}, MRCLASS = {16Exx (52C35)}, MRNUMBER = {1911506 (2003k:52022)}, MRREVIEWER = {Ruth Lawrence}, ZBLNUMBER = {1057.52015}, KEYWORDS = {lower central series; free resolution; hyperplane arrangement; change of rings spectral sequence; Koszul algebra; linear strand; graphic arrangement}, abstract = {}, ID_AR = {math.AG/0109070}, URL = {http://www.ams.org/journal-getitem?pii=S0002-9947-02-03021-0}, DOI = {10.1090/S0002-9947-02-03021-0} } @article {Suciu:imrn02, AUTHOR = {Matei, Daniel and Suciu, Alexander I.}, TITLE = {Hall invariants, homology of subgroups, and characteristic varieties}, JOURNAL = {Int. Math. Res. Not.}, FJOURNAL = {International Mathematics Research Notices}, YEAR = {2002}, NUMBER = {9}, PAGES = {465--503}, ISSN = {1073-7928}, MRCLASS = {20Fxx (20J05)}, MRNUMBER = {1884468 (2003d:20055)}, MRREVIEWER = {Alexander Lubotsky}, ZBLNUMBER = {1061.20040}, KEYWORDS = {Hall invariants, metabelian groups, characteristic varieties, cohomology of groups, low-index subgroups, fundamental groups}, abstract = {Given a finitely-generated group $G$, and a finite group $\Gamma$, Philip Hall defined $\delta_{\Gamma(G)}$ to be the number of factor groups of $G$ that are isomorphic to $\Gamma$. We show how to compute the Hall invariants by cohomological and combinatorial methods, when $G$ is finitely-presented, and $\Gamma$ belongs to a certain class of metabelian groups. Key to this approach is the stratification of the character variety, ${\rm Hom}(G,\mathbb{K}^*)$, by the jumping loci of the cohomology of $G$, with coefficients in rank $1$ local systems over a suitably chosen field $\mathbb{K}$. Counting relevant torsion points on these ``characteristic'' subvarieties gives $\delta_{\Gamma(G)}$. In the process, we compute the distribution of prime-index, normal subgroups $K\triangleleft G$ according to $\dim_{\mathbb{K}} H_1(K;\mathbb{K})$, provided ${\rm char}\, \mathbb{K}\ne |G:K|$. In turn, we use this distribution to count low-index subgroups of $G$. We illustrate these techniques in the case when $G$ is the fundamental group of the complement of an arrangement of either affine lines in $\mathbb{C}^{2}$, or transverse planes in $\mathbb{R}^4$.}, ID_AR = {math.GR/0010046}, URL = {http://imrn.oxfordjournals.org/cgi/content/abstract/2002/9/465}, DOI = {10.1155/S107379280210907X} } @article {Suciu:adv02, AUTHOR = {Papadima, Stefan and Suciu, Alexander I.}, TITLE = {Higher homotopy groups of complements of complex hyperplane arrangements}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {165}, YEAR = {2002}, month = {jan}, NUMBER = {1}, PAGES = {71--100}, ISSN = {0001-8708}, MRCLASS = {55R80 (32S22 52C35)}, MRNUMBER = {1880322 (2003b:55019)}, MRREVIEWER = {Daniel C. Cohen}, ZBLNUMBER = {1019.52016}, ZBREVIEWER = {Michael J. Falk}, KEYWORDS = {hypersolvable arrangement, higher homotopy groups, minimal cell decomposition}, abstract = {We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range, and we give an explicit $\mathbb{Z}\pi_1$-module presentation of $\pi_p$, the first non-vanishing higher homotopy group. We also give a combinatorial formula for the $\pi_1$-coinvariants of $\pi_p$. For affine line arrangements whose cones are hypersolvable, we provide a minimal resolution of $\pi_2$, and study some of the properties of this module. For graphic arrangements associated to graphs with no $3$-cycles, we obtain information on $\pi_2$, directly from the graph. The $\pi_1$-coinvariants of $\pi_2$ may distinguish the homotopy $2$-types of arrangement complements with the same $\pi_1$, and the same Betti numbers in low degrees.}, ID_AR = {math.AT/0002251}, DOI = {10.1006/aima.2001.2023} } @incollection {Suciu:conm01, AUTHOR = {Suciu, Alexander I.}, TITLE = {Fundamental groups of line arrangements: Enumerative aspects}, BOOKTITLE = {Advances in algebraic geometry motivated by physics (Lowell, MA, 2000)}, SERIES = {Contemp. Math.}, FSERIES = {Contemporary Mathematics}, VOLUME = {276}, PAGES = {43--79}, EDITOR = {Emma Previato}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2001}, MRCLASS = {14F35 (32S22 52C35 57M05)}, MRNUMBER = {1837109 (2002k:14029)}, MRREVIEWER = {Nguyen Viet Dung}, ZBLNUMBER = {0998.14012}, KEYWORDS = {complements of line arrangements; fundamental groups; characteristic varieties; resonance varieties; finite covers}, ID_AR = {math.AG/0010105} } @article {Suciu:topapp02, AUTHOR = {Suciu, Alexander I.}, TITLE = {Translated tori in the characteristic varieties of complex hyperplane arrangements}, NOTE = {Arrangements in Boston: a Conference on Hyperplane Arrangements (1999)}, JOURNAL = {Topology Appl.}, FJOURNAL = {Topology and its Applications}, VOLUME = {118}, YEAR = {2002}, NUMBER = {1-2}, PAGES = {209--223}, ISSN = {0166-8641}, MRCLASS = {32S22 (52C35)}, MRNUMBER = {1877726 (2002j:32027)}, MRREVIEWER = {Guangfeng Jiang}, ZBLNUMBER = {1021.32009}, ZBREVIEWER = {Margaret M. Bayer}, KEYWORDS = {hyperplane arrangement; characteristic variety; Orlik-Solomon algebra; translated tori}, abstract = {}, ID_AR = {math.AG/9912227}, DOI = {10.1016/S0166-8641(01)00052-9} } @book {Suciu:arrbos02, TITLE = {Arrangements in {B}oston: a {C}onference on {H}yperplane {A}rrangements}, EDITOR = {Cohen, Daniel C. and Suciu, Alexander I.}, NOTE = {Papers from the conference held at Northeastern University, Boston, MA, June 12--15, 1999, Topology Appl. {\bf 118} (2002), no. 1-2}, PUBLISHER = {North-Holland Publishing Co.}, ADDRESS = {Amsterdam}, YEAR = {2002}, PAGES = {v--viii and 1--274}, ISSN = {0166-8641}, MRCLASS = {00B25 (20-06 52-06)}, MRNUMBER = {1877711 (2002h:00013)}, ZBLNUMBER = {0983.00038}, DOI = {10.1016/S0166-8641(01)00055-4} } @article {Suciu:gafa01, AUTHOR = {Katz, Mikhail G. and Suciu, Alexander I.}, TITLE = {Systolic freedom of loop space}, JOURNAL = {Geom. Funct. Anal.}, FJOURNAL = {Geometric and Functional Analysis}, VOLUME = {11}, YEAR = {2001}, NUMBER = {1}, PAGES = {60--73}, ISSN = {1016-443X}, MRCLASS = {53C23 (55M99)}, MRNUMBER = {1829642 (2002c:53067)}, MRREVIEWER = {John F. Oprea}, ZBLNUMBER = {1048.53030}, ZBREVIEWER = {H. Gollek}, KEYWORDS = {systolic freedom; systole; total volume; submanifold; loop space; rational homotopy}, abstract = {}, ID_AR = {math.DG/0106153}, URL = {http://www.springerlink.com/content/8xf1kr4b43ratj08/}, DOI = {10.1007/PL00001672} } @incollection {Suciu:aspm00, AUTHOR = {Matei, Daniel and Suciu, Alexander I.}, TITLE = {Cohomology rings and nilpotent quotients of real and complex arrangements}, BOOKTITLE = {Arrangements---Tokyo 1998}, SERIES = {Adv. Stud. Pure Math.}, FSERIES = {Advanced Studies in Pure Mathematics}, VOLUME = {27}, PAGES = {185--215}, PUBLISHER = {Kinokuniya}, ADDRESS = {Tokyo}, YEAR = {2000}, EDITOR = {Michael Falk and Hiroaki Terao}, MRCLASS = {32S22 (20F34 55R80)}, MRNUMBER = {1796900 (2002b:32045)}, MRREVIEWER = {Nguyen Viet Dung}, ZBLNUMBER = {0974.32020}, KEYWORDS = {cohomology rings; nilpotent quotients; real and complex hyperplane arrangements; {O}rlik-{S}olomon algebra}, abstract = {For an arrangement with complement $X$ and fundamental group $G$, we relate the truncated cohomology ring, $H^{\le 2}(X)$, to the second nilpotent quotient, $G/G_3$. We define invariants of $G/G_3$ by counting normal subgroups of a fixed prime index $p$, according to their abelianization. We show how to compute this distribution from the resonance varieties of the {O}rlik-{S}olomon algebra mod $p$. As an application, we establish the cohomology classification of $2$-arrangements of $n\le 6$ planes in $\mathbb{R}^4$.}, ID_AR = {math.GT/9812087}, } @article {Suciu:camb99, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {Characteristic varieties of arrangements}, JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society}, VOLUME = {127}, YEAR = {1999}, NUMBER = {1}, PAGES = {33--53}, ISSN = {0305-0041}, MRCLASS = {32S22 (52C35)}, MRNUMBER = {1692519 (2000m:32036)}, MRREVIEWER = {Hiroaki Terao}, ZBLNUMBER = {0963.32018}, KEYWORDS = {arrangement of complex hyperplanes; characteristic subvariety; Alexander invariants; reflection arrangements; monomial groups}, abstract = {}, ID_AR = {math.AG/9801048}, URL = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=37609}, DOI = {10.1017/S0305004199003576}, GSID = {7302019678268589445} } @incollection {Suciu:conm99, AUTHOR = {Katz, Mikhail G. and Suciu, Alexander I.}, TITLE = {Volume of {R}iemannian manifolds, geometric inequalities, and homotopy theory}, BOOKTITLE = {Tel Aviv Topology Conference: Rothenberg Festschrift (1998)}, SERIES = {Contemp. Math.}, VOLUME = {231}, PAGES = {113--136}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1999}, EDITOR = {Michael Farber, Wolfgang L{\"u}ck, Shmuel Weinberger}, MRCLASS = {53C23 (55Q15)}, MRNUMBER = {1705579 (2000i:53063)}, MRREVIEWER = {Andrea Sambusetti}, ZBLNUMBER = {0967.53024}, ZBREVIEWER = {Vladimir Yu. Rovenskij}, KEYWORDS = {volume; stable systole; systolic freedom; coarea inequality; isoperimetric inequality; surgery; Whitehead product; loop space; {E}ilenberg-{M}ac{L}ane space; ordinary systole}, abstract = {}, ID_AR = {math.DG/9810172} } @article {Suciu:top00, AUTHOR = {Matei, Daniel and Suciu, Alexander I.}, TITLE = {Homotopy types of complements of {$2$}-arrangements in {${\mathbf{R}}\sp 4$}}, JOURNAL = {Topology}, FJOURNAL = {Topology. An International Journal of Mathematics}, VOLUME = {39}, YEAR = {2000}, NUMBER = {1}, PAGES = {61--88}, ISSN = {0040-9383}, MRCLASS = {55R80 (52C35)}, MRNUMBER = {1710992 (2000h:55028)}, MRREVIEWER = {Peter Orlik}, Zblnumber = {0940.55010}, Zbreviewer = {Vincent Moulton}, keywords = {arrangement; line configuration; link; braid; characteristic variety}, abstract = {}, ID_AR = {math.GT/9712251}, DOI = {10.1016/S0040-9383(98)00058-5} } @article {Suciu:mrl98, AUTHOR = {Babenko, Ivan K. and Katz, Mikhail G. and Suciu, Alexander I.}, TITLE = {Volumes, middle-dimensional systoles, and {W}hitehead products}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {5}, YEAR = {1998}, NUMBER = {4}, PAGES = {461--471}, ISSN = {1073-2780}, MRCLASS = {53C23 (53C20 55Q15)}, MRNUMBER = {1653310 (99m:53084)}, MRREVIEWER = {Athanase Papadopoulos}, ZBLNUMBER = {0933.53022}, ZBREVIEWER = {A. P. Stone}, KEYWORDS = {Whitehead product; $k$-systole; systolic freedom}, abstract = {}, ID_AR = {math.DG/9707116}, URL = {http://www.mrlonline.org/mrl/1998-005-004/1998-005-004-004.pdf} } @article {Suciu:tams99, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {Alexander invariants of complex hyperplane arrangements}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {351}, YEAR = {1999}, NUMBER = {10}, PAGES = {4043--4067}, ISSN = {0002-9947}, MRCLASS = {52B30 (20F34 57M05)}, MRNUMBER = {1475679 (99m:52019)}, MRREVIEWER = {Richard Randell}, ZBLNUMBER = {0945.20024}, ZBREVIEWER = {V. V. Chueshev}, KEYWORDS = {Alexander invariants; {C}hen groups; {G}assner representation; fundamental groups; braid monodromy homomorphisms; pure braid groups; presentations}, abstract = {}, ID_AR = {math.AG/9703030}, URL = {http://www.ams.org/tran/1999-351-10/S0002-9947-99-02206-0/}, DOI = {10.1090/S0002-9947-99-02206-0} } @article {Suciu:jpaa98, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {Homology of iterated semidirect products of free groups}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {126}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {87--120}, ISSN = {0022-4049}, MRCLASS = {20J05 (20F36 57M05)}, MRNUMBER = {1475679 (99e:20064)}, MRREVIEWER = {Paul Igodt}, ZBLNUMBER = {0908.20033}, ZBREVIEWER = {Michael J. Falk}, KEYWORDS = {Group cohomology; braid groups; fundamental groups; fiber-type arrangements; {M}ilnor fibers; cohomology vanishing theorems; Coxeter arrangements; {B}urau and {G}assner representations}, abstract = {}, ID_AR = {math.AG/9503002}, DOI = {10.1016/S0022-4049(96)00153-3} } @article {Suciu:cmh97, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {The braid monodromy of plane algebraic curves and hyperplane arrangements}, JOURNAL = {Comment. Math. Helv.}, FJOURNAL = {Commentarii Mathematici Helvetici}, VOLUME = {72}, YEAR = {1997}, NUMBER = {2}, PAGES = {285--315}, ISSN = {0010-2571}, MRCLASS = {52B30 (14H30 20F36 57M05)}, MRNUMBER = {1470093 (98f:52012)}, MRREVIEWER = {Lee Rudolph}, ZBLNUMBER = {0959.52018}, ZBREVIEWER = {A. Lipovski}, KEYWORDS = {Braid monodromy; plane algebraic curve; hyperplane arrangement; fundamental group of the complement of an algebraic curve; polynomial cover; braid group; wiring diagram; intersection lattice}, abstract = {To a plane algebraic curve of degree $n$, {M}oishezon associated a braid monodromy homomorphism from a finitely generated free group to {A}rtin's braid group $B_n$. Using {H}ansen's polynomial covering space theory, we give a new interpretation of this construction. Next, we provide an explicit description of the braid monodromy of an arrangement of complex affine hyperplanes, by means of an associated ``braided wiring diagram.'' The ensuing presentation of the fundamental group of the complement is shown to be {T}ietze-I equivalent to the {R}andell-{A}rvola presentation. Work of {L}ibgober then implies that the complement of a line arrangement is homotopy equivalent to the $2$-complex modeled on either of these presentations. Finally, we prove that the braid monodromy of a line arrangement determines the intersection lattice. Examples of {F}alk then show that the braid monodromy carries more information than the group of the complement, thereby answering a question of {L}ibgober.}, ID_AR = {math.AG/9608001}, URL = {http://www.springerlink.com/content/h9aamqbq1704rn6d/}, DOI = {10.1007/s000140050017}, GSID = {8881203904084384409} } @article {Suciu:jpaa95, AUTHOR = {Farjoun, Emmanuel Dror and Jekel, Solomon M. and Suciu, Alexander I.}, TITLE = {Homology of jet groups}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {102}, YEAR = {1995}, month = {jul}, NUMBER = {1}, PAGES = {17--24}, ISSN = {0022-4049}, MRCLASS = {20J05}, MRNUMBER = {1350206 (97g:20060)}, MRREVIEWER = {}, ZBLNUMBER = {0848.57036}, ZBREVIEWER = {John McCleary}, KEYWORDS = {Jet groups; spectral sequence; group homology}, abstract = {In this paper we compute the second homology of the discrete jet groups. The $n$-th jet group, $J_n$, is the group, under composition followed by truncation, of invertible, orientation-preserving real $n$-jets at $0$. Consider the homomorphism $D: J_n \to \mathbb{R}^+$ obtained by projecting onto the first coefficient. The main result of this paper is: The map $D_*: H_2(J_n) \to H_2(\mathbb{R}^+)$ is an isomorphism.}, DOI = {10.1016/0022-4049(95)00055-2} } @article {Suciu:jlms95, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {On {M}ilnor fibrations of arrangements}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {51}, YEAR = {1995}, NUMBER = {1}, PAGES = {105--119}, ISSN = {0024-6107}, MRCLASS = {32S55 (52B30)}, MRNUMBER = {1310725 (96e:32034)}, MRREVIEWER = {Richard Randell}, ZBLNUMBER = {0814.32007}, ZBREVIEWER = {Daniel C.Cohen}, KEYWORDS = {{M}ilnor fiber; homogeneous polynomial; hyperplane arrangements; Betti numbers; algebraic monodromy}, abstract = {We use covering space theory and homology with local coefficients to study the {M}ilnor fiber of a homogeneous polynomial. These techniques are applied in the context of hyperplane arrangements, yielding an explicit algorithm for computing the {B}etti numbers of the {M}ilnor fiber of an arbitrary real central arrangement in $C^3$, as well as the dimensions of the eigenspaces of the algebraic monodromy. We also obtain combinatorial formulas for these invariants of the {M}ilnor fiber of a generic arrangement of arbitrary dimension using these methods.}, URL = {http://jlms.oxfordjournals.org/cgi/content/abstract/51/1/105}, DOI = {10.1112/jlms/51.1.105} } @incollection {Suciu:conm95, AUTHOR = {Cohen, Daniel C. and Suciu, Alexander I.}, TITLE = {The {C}hen groups of the pure braid group}, BOOKTITLE = {The {\v{C}}ech centennial (Boston, MA, 1993)}, SERIES = {Contemp. Math.}, VOLUME = {181}, PAGES = {45--64}, EDITOR = {Mila Cenkl and Haynes Miller}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1995}, MRCLASS = {20F14 (20F36 57M25)}, MRNUMBER = {1320987 (96c:20055)}, MRREVIEWER = {Colin Maclachlan}, ZBLNUMBER = {0833.20047}, ZBREVIEWER = {A. M. Akimenkov}, KEYWORDS = {lower central series, {C}hen groups, pure braid groups, Hilbert series, graded modules, Gr{\"{o}}bner bases}, abstract = {The {C}hen groups of a group are the lower central series quotients of its maximal metabelian quotient. We show that the {C}hen groups of the pure braid group $P_n$ are free abelian, and we compute their ranks. The computation of these {C}hen groups reduces to the computation of the {H}ilbert series of a certain graded module over a polynomial ring, and the latter is carried out by means of a {G}r{\"{o}}bner basis algorithm. This result shows that, for $n \ge 4$, the group $P_n$ is not a direct product of free groups.}, URL = {http://www.math.neu.edu/~suciu/papers/chenpn.pdf} } @article{Suciu:bams93, AUTHOR = {Dwyer, William G. and Jekel, Solomon M. and Suciu, Alexander I.}, TITLE = {Homology isomorphisms between algebraic groups made discrete}, JOURNAL = {Bull. London Math. Soc.}, FJOURNAL = {The Bulletin of the London Mathematical Society}, VOLUME = {25}, YEAR = {1993}, NUMBER = {2}, PAGES = {145--149}, ISSN = {0024-6093}, MRCLASS = {20J05 (57T99)}, MRNUMBER = {1204066 (94f:20097)}, MRREVIEWER = {Lekh Raj Vermani}, ZBLNUMBER = {0801.20017}, ZBREVIEWER = {Li Fuan}, KEYWORDS = {homology groups; split exact sequence; discrete groups; diagonalizable endomorphism; connected affine algebraic group; unipotent radical; descending central series}, abstract = {Consider a split exact sequence of discrete groups $$\{1\}\to G \to \Gamma \overset\pi\to {\underset\sigma\to\rightleftarrows} \Gamma/G \to \{1\}.$$ Suppose there exists a normal series $G=G_0 \triangleright G_1 \triangleright \cdots \triangleright G_n \triangleright G_{n+1}={1}$, such that (1) $G_i/G_{i+1}$ is a rational vector space for $i=0, cdots, n$; (2) $G_i/G_{i+1}$ is contained in the center of $G/G_{i+1}$ for $i=0, cdots, n$; (3) there exists an element in the center of $\Gamma/G$ that induces a diagonalizable endomorphism of each $G_i/G_{i+1}$ with all eigenvalues rational and greater than $1$. Then the map $pi$ induces an isomorphism $pi_* \colon H_*(B \Gamma,Z) \to H_*(B (\Gamma/G), \mathbb{Z})$.}, URL = {http://blms.oxfordjournals.org/cgi/reprint/25/2/145}, DOI = {10.1112/blms/25.2.145} } @article {Suciu:cmh92, AUTHOR = {Suciu, Alexander I.}, TITLE = {Inequivalent frame-spun knots with the same complement}, JOURNAL = {Comment. Math. Helv.}, FJOURNAL = {Commentarii Mathematici Helvetici}, VOLUME = {67}, YEAR = {1992}, month = {dec}, NUMBER = {1}, PAGES = {47--63}, ISSN = {0010-2571}, MRCLASS = {57Q45}, MRNUMBER = {1144613 (93a:57026)}, MRREVIEWER = {Jerome P. Levine}, ZBLNUMBER = {789.57014}, ZBREVIEWER = {Cherry Kearton}, KEYWORDS = {High-dimensional knots, frame-spinning construction, generalized {P}ontryagin-{T}hom construction, homotopy groups of spheres, {G}luck twist, inequivalent knots with the same complement}, abstract = {}, URL = {http://www.springerlink.com/content/k2054n6263477407/}, URL = {http://retro.seals.ch/digbib/view?rid=comahe-003:1992:67::9}, DOI = {10.1007/BF02566488} } @article {Suciu:mathann91, AUTHOR = {Klein, John R. and Suciu, Alexander I.}, TITLE = {Inequivalent fibred knots whose homotopy {S}eifert pairings are isometric}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {289}, YEAR = {1991}, month = {mar}, NUMBER = {4}, PAGES = {683--701}, ISSN = {0025-5831}, MRCLASS = {57Q45}, MRNUMBER = {1103043 (92d:57015)}, MRREVIEWER = {Cherry Kearton}, ZBLNUMBER = {711.57015}, KEYWORDS = {}, abstract = {}, URL = {http://www.springerlink.com/content/k2k262hp36m74124/}, DOI = {10.1007/BF01446596} } @article {Suciu:tams90, AUTHOR = {Suciu, Alexander I.}, TITLE = {Iterated spinning and homology spheres}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {321}, YEAR = {1990}, month = {sep}, NUMBER = {1}, PAGES = {145--157}, ISSN = {0002-9947}, MRCLASS = {57N65 (55Q52 57Q45 57R19)}, MRNUMBER = {987169 (90m:57014)}, MRREVIEWER = {Laurence R. Taylor}, ZBLNUMBER = {725.57010}, ZBREVIEWER = {Jerome P. Levine}, KEYWORDS = {Spinning manifolds; homology spheres; homotopy type}, abstract = {Given a closed $n$-manifold $M^n$ and a tuple of positive integers $P$, let $\sigma_P M$ be the $P$-spin of $M$. If $M \not\simeq S^n$ and $P\ne Q$ (as unordered tuples), it is shown that $\sigma_P M \not\simeq \sigma_Q M$ if either (1) $H_*(M) \not\cong H_*(S^n)$, (2) $\pi_1(M)$ is finite, (3) $M$ is aspherical, or (4) $n=3$. Applications to the homotopy classification of homology spheres and knot exteriors are given.}, URL = {http://www.ams.org/journals/tran/1990-321-01/S0002-9947-1990-0987169-3/}, DOI = {10.1090/S0002-9947-1990-0987169-3} } @article {Suciu:pac88, AUTHOR = {Suciu, Alexander I.}, TITLE = {The oriented homotopy type of spun {$3$}-manifolds}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {131}, YEAR = {1988}, NUMBER = {2}, PAGES = {393--399}, ISSN = {0030-8730}, MRCLASS = {57N13 (55P15 57M99)}, MRNUMBER = {922225 (89d:57020)}, MRREVIEWER = {Cameron McA. Gordon}, ZBLNUMBER = {594.57008}, ZBREVIEWER = {}, KEYWORDS = {Spinning 3-manifolds, homotopy type}, abstract = {}, URL = {http://projecteuclid.org/euclid.pjm/1102689936} } @article {Suciu:mz87, AUTHOR = {Suciu, Alexander I.}, TITLE = {Immersed spheres in {$\mathbf{CP}\sp 2$} and {$S\sp 2\times S\sp 2$}}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {196}, YEAR = {1987}, month = {mar}, NUMBER = {1}, PAGES = {51--57}, ISSN = {0025-5874}, MRCLASS = {57R95 (57N13 57R42)}, MRNUMBER = {907407 (88j:57038)}, MRREVIEWER = {Don{\v{c}}o Dimovski}, ZBLNUMBER = {608.57025}, ZBREVIEWER = {}, KEYWORDS = {Four-manifolds, immersed spheres, intersection form}, abstract = {If $M$ is a compact, connected, simply-connected, smooth $4$-manifold, and gamma is a class in $H_2(M; \mathbb{\Z})$, define $d_{\gamma}$ to be the minimum number of double points of immersed spheres representing $\gamma$. We use a theorem of S. K. Donaldson to provide lower bounds for $d_{\gamma}$, for $\gamma$ certain homology classes in rational surfaces.}, URL = {http://www.springerlink.com/content/gg5677l137p214h3/}, DOI = {10.1007/BF01179266} } @article {Suciu:jlms87, AUTHOR = {Plotnick, Steven P. and Suciu, Alexander I.}, TITLE = {Fibered knots and spherical space forms}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {35}, YEAR = {1987}, NUMBER = {3}, PAGES = {514--526}, ISSN = {0024-6107}, MRCLASS = {57Q45}, MRNUMBER = {889373 (88f:57038)}, MRREVIEWER = {Jonathan A. Hillman}, ZBLNUMBER = {587.57009}, ZBREVIEWER = {}, KEYWORDS = {}, abstract = {}, URL = {http://jlms.oxfordjournals.org/cgi/reprint/s2-35/3/514.pdf}, DOI = {10.1112/jlms/s2-35.3.514} } @article {Suciu:topapp87, AUTHOR = {Suciu, Alexander I.}, TITLE = {Homology $4$-spheres with distinct $k$-invariants}, JOURNAL = {Topology Appl.}, FJOURNAL = {Topology and its Applications}, VOLUME = {25}, YEAR = {1987}, month = {feb}, NUMBER = {1}, PAGES = {103--110}, ISSN = {0166-8641}, MRCLASS = {57N13 (55S45 57Q45 57R65)}, MRNUMBER = {874982 (88f:57021)}, MRREVIEWER = {Don{\v{c}}o Dimovski}, ZBLNUMBER = {617.57008}, ZBREVIEWER = {Dusan Repov\v{s}}, KEYWORDS = {Homology 4-spheres, k-invariants}, abstract = {We exhibit integral-homology $4$-spheres with isomorphic $pi_1$ and $pi_2$ (as $pi_1$-modules), but with distinct $k$-invariants.}, DOI = {10.1016/0166-8641(87)90079-4} } @article {Suciu:camb85, AUTHOR = {Suciu, Alexander I.}, TITLE = {Infinitely many ribbon knots with the same fundamental group}, JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society}, VOLUME = {98}, YEAR = {1985}, NUMBER = {3}, PAGES = {481--492}, ISSN = {0305-0041}, MRCLASS = {57Q45 (57M05)}, MRNUMBER = {803607 (87a:57025)}, MRREVIEWER = {Don{\v{c}}o Dimovski}, ZBLNUMBER = {596.57013}, ZBREVIEWER = {Yasutaka Nakanishi}, KEYWORDS = {Knots in the 4-sphere, homotopy groups}, abstract = {A knot $K = (S^{n+2}, S^{n})$ is a ribbon knot if $S^{n}$ bounds an immersed disc $D^{n+1}$ in $S^{n+2}$ with no triple points and such that the components of the singular set are $n$-discs whose boundary $(n-1)$-spheres either lie on $S^{n}$ or are disjoint from $S^{n}$. Pushing $D^{n+1}$ into $D^{n+3}$ produces a ribbon disc pair $D = (D^{n+3}, D^{n+1})$, with the ribbon knot $(S^{n+2}, S^{n})$ on its boundary. The double of a ribbon $(n+1)$-disc pair is an $(n+1)$-ribbon knot. Every $(n+1)$-ribbon knot is obtained in this manner.}, URL = {http://journals.cambridge.org/action/displayAbstract?aid=2095324}, DOI = {10.1017/S0305004100063684} } @article {Suciu:cmh85, AUTHOR = {Plotnick, Steven P. and Suciu, Alexander I.}, TITLE = {{$k$}-invariants of knotted {$2$}-spheres}, JOURNAL = {Comment. Math. Helv.}, FJOURNAL = {Commentarii Mathematici Helvetici}, VOLUME = {60}, YEAR = {1985}, month = {dec}, NUMBER = {1}, PAGES = {54--84}, ISSN = {0010-2571}, MRCLASS = {57Q45 (55P15)}, MRNUMBER = {787662 (86i:57026)}, MRREVIEWER = {John G. Ratcliffe}, ZBLNUMBER = {568.57017}, ZBREVIEWER = {Cherry Kearton}, KEYWORDS = {Knots in the 4-sphere, homotopy type}, abstract = {This paper studies some questions concerning homotopy type invariants of smooth four-dimensional knot complements. Higher-dimensional knot theory diverges sharply from classical knot theory in this respect. A knot complement $S^4\setminus S^2$ has the homotopy type of a $3$-complex, so a natural question is whether the homotopy theory of knot complements in $S^4$ can be as complicated as that of arbitrary $3$-complexes. The main result of this paper indicates that the answer is yes.}, URL = {http://www.springerlink.com/content/q7440uh56552136t}, DOI = {10.1007/BF02567400} } @phdthesis{Suciu:thesis, author = {Suciu, Alexander I.}, title = {Homotopy Type Invariants of Four-Dimensional Knot Complements}, school = {Columbia University}, address = {New York, NY}, year = {1984}, month = {may}, note = {Ph.D. thesis. Photocopy: UMI-8427479, Ann Arbor, MI}, keywords = {Knots in the 4-sphere, homotopy type}, abstract = {This thesis studies the homotopy type of smooth four dimensional knot complements. In contrast with the classical case, high-dimensional knot complements with fundamental group different from are never aspherical. The second homotopy group already provides examples of the way in which a knot in $S^4$ can fail to be determined by its fundamental group ({C}. {M}c{A}. Gordon, {S}. {P}. {P}lotnick). A natural class of knots to investigate is ribbon knots. They bound immersed disks with ``ribbon singularities''. A method is given for computing $\pi_2$ of such knot complements. I show that there are infinitely many ribbon knots in $S^4$ with isomorphic $\pi_1$ but distinct $\pi_2$ (viewed as $\pi_1$-modules). They appear as boundaries of distinct ribbon disk pairs with the same exterior. These knots have the fundamental group of the spun trefoil, but none in a spun knot. To a four-dimensional knot complement, one can associate a certain cohomology class, the first $k$-invariant of {E}ilenberg, {M}ac{L}ane and {W}hitehead. In a joint paper, {P}lotnick and I showed that there are arbitrarily many knots in $S^4$ whose complements have isomorphic $\pi_1$ and $\pi_2$ (as $\pi_1$-modules), but distinct $k$-invariants. Here I prove this result using examples which are somewhat more natural and easier to produce. They are constructed from a fibered knot with fiber a punctured lens space and a ribbon knot by surgery. The proofs involve writing down explicit cell complexes, computing twisted cohomology groups, combinatorial group theory and calculations in group rings.}, URL = {http://proquest.umi.com/pqdlink?did=751356951&Fmt=7&clientId =79356&RQT=309&VName=PQD} }