Prof. Alex Suciu
MATH 7375 · Topics in Topology
Cohomology Jumping Loci
Mon & Wed 7:30pm to 9pm in 105 RY
The cohomology jumping loci of a space X come in two
basic flavors: the characteristic varieties (the jump loci for
cohomology with coefficients in rank 1 local systems),
and the resonance varieties (the jump loci for the homology
of the cochain complexes arising from multiplication by
degree 1 classes in the cohomology ring of X).
The interplay between these varieties leads to new obstructions
to formality and (quasi-) projectivity, and informs
on the homological finiteness properties of various spaces and groups.
- A. Dimca, A. Suciu, Which 3-manifold groups are Kähler groups?,
J. Eur. Math. Soc. 11 (2009), no. 3, 521-528.
- A. Dimca, S. Papadima, A. Suciu, Topology and geometry of cohomology jump loci,
Duke Math. J. 148 (2009), no. 3, 405-457.
- A. Dimca, S. Papadima, A. Suciu, Non-finiteness properties of fundamental groups of smooth projective varieties,
J. Reine Angew. Math 629 (2009), 89-105.
- S. Papadima, A. Suciu, The spectral sequence of an equivariant chain complex and homology with local coefficients,
Trans. Amer. Math. Soc. 362 (2010), no. 5, 2685-2721.
- S. Papadima, A. Suciu, Bieri-Neumann-Strebel-Renz invariants and homology jumping loci,
Proc. London Math. Society (2010).
- S. Papadima, A. Suciu, Algebraic monodromy and obstructions to formality, Forum Math. (2010).
- A. Suciu, Fundamental groups, Alexander invariants, and cohomology jumping loci,