|
MTH G321 · Topology 3
Spring 2009
Tuesday 10:00am to 11:30am
Thursday 2:40pm to 4:10pm
in 544 NI
|
|
This is a course in classical Algebraic Topology, and some of its applications. Topics we may cover include: Higher homotopy groups, cofibrations, fibrations, fiber bundles, homotopy sequences, homotopy groups of Lie groups and associated manifolds, cellular approximation, Hurewicz theorem, Whitehead theorem, Eilenberg-MacLane spaces, obstruction theory, Postnikov towers, H-spaces and Hopf algebras, Bockstein homomorphism, Poincaré-Lefschetz duality, Alexander duality, Euler class, Gysin sequence, cobordism, intersection form, signature, plumbing, cohomology of fiber bundles, classifying spaces, characteristic classes, spectral sequences, Steenrod squares.
|
|
We will cover material from the following textbooks:
|
-
Lecture Notes in Algebraic Topology, by James F. Davis and Paul Kirk, Graduate Studies in Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2001. MR.
-
Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2002. MR.
-
Topology and Geometry, by Glen Bredon, GTM No. 139, Springer-Verlag, 1997.
MR.
-
A Concise Course in Algebraic Topology, by J. Peter May,
Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1999.
MR.
|
|
Here are some other useful references, and material for further reading:
|
-
Elements of Homotopy Theory, by George W. Whitehead, GTM No. 61, Springer-Verlag, 1979. MR.
-
A user's guide to spectral sequences, by John McCleary, second edition, Cambridge Studies in Advanced Math, no. 58, Cambridge University Press, 2001. MR.
-
Characteristic Classes, by John W. Milnor and James Stasheff, Ann. Math. Studies, No. 76, Princeton University Press, 1973. MR.
-
Algebraic Topology, by Edwin H. Spanier, Corrected reprint, Springer-Verlag, 1981. MR.
-
The topology of fibre bundles , by Norman Steenrod, reprint of 1951 edition, Princeton University Press, 1999. MR.
-
Spectral Sequences in Algebraic Topology, by Allen Hatcher, draft book, 2004.
|
 Homework assignments
|
|
a.suciu@neu.edu
