MATH 753: Characteristic Classes (Fall 2006)

Instructor: Peter Kahn

Meeting Time & Room

Prerequisite: MATH 651 or permission of the instructor.

Textbook: Characteristic Classes, Milnor and Stasheff, Prin. U. Press, 1974.

The theory of characterisic classes occupies the interface between algebraic and differential topology. Most of the major advances in differential topology over the past fifty years have involved characteristic classes in some way. John Milnor's 1957 course on characteristic classes, appearing in 1974 as a book, was an enormously influential — and arguably still the best — introduction to the subject.

This course will cover as much of the book as time permits, including important topics such as vector bundles, Stiefel-Whitney classes, Grassmann manifolds, Euler classes, Chern classes, Pontrjagin classes, and cobordism. To form a bridge with Math 651, the course will start with background material from Appendix A of the book: a brief introduction to cohomology theory and its connection with homology.

Last modified: April 25, 2006