MATH 7530 - Algebraic Topology II

Reyer Sjamaar, fall 2014.

This is the continuation of the introductory algebraic topology course 6510. Most topics will be chosen from the second half of Hatcher's book Algebraic Topology, centering around cohomology and homotopy theory, including such things as cup products in cohomology, Künneth formulas, excision for homotopy groups, the Hurewicz theorem, cellular and CW approximation, fiber bundles and fibrations, and Eilenberg-MacLane spaces.

The textbook can be downloaded for free on http://www.math.cornell.edu/~hatcher/

Note added July 2014. There turns out to be a high popular demand for a course on characteristic classes. I am happy to comply with this demand, but to do this I have to reorganize the course. My current plan is to follow in outline Characteristic classes by Milnor and Stasheff (part of which is available on Google Books), which starts more or less from scratch and ends with the Hirzebruch signature theorem. Fine as it is, the book is a bit dated, so I will also try to draw from more recent sources. I plan to include quick introductions to cohomology theory and fibre bundles.