Math 2420 Algebraic Topology, Spring 2012

Course Information

A printable pdf version of the syllabus is here.

Basic Information

Instructor: Chris Kottke

Office: 303 Kassar-Gould House


Office hours: WF 2-3pm, or by appointment.

Text: Algebraic Topology, by Allen Hatcher. ISBN: 0-521-79540-0. Also freely available from the author's website

Other useful texts (not required):

Grading: Your final grade will depend on 5-6 (approximately biweekly) homework assignments, and (tentatively) a take-home final exam, weighted as follows.


Assuming knowledge of the fundamental group and singular homology, in the first part of the class we will cover singular cohomology, including the cup product and Poincare duality following Hatcher. The second portion of the class will include a brief introduction to homotopy theory, followed by a study characteristic classes and classifying spaces, emphasizing the theory of principal bundles. We will discuss Stiefel-Whitney, Euler and Chern classes, hopefully culminating in some discussion of cobordism.

The second half of the class will involve material not in Hatcher, for which notes will be produced by the instructor.

Tentative outline:

1Homology odds and ends.
2Definition and properties of cohomology.
3Universal coefficient theorem for homology and cohomology, Ext and Tor.
4-5Cup product, Kunneth theorems.
6-7Poincare duality.
8Higher homotopy groups, cellular approximation, weak equivalence.
9Loops and suspensions, Puppe sequence and general cohomology theories.
10Vector bundles and principal bundles.
11Universal bundles and characteristic classes.
12SO and Stiefel-Whitney classes.
13U and Chern classes.
14Thom construction and cobordism.