# Math 6530, Fall 2017

## K-theory and characteristic classes

This class is an introduction to topological K-theory and characteristic
classes. Topological K-theory is a generalized cohomology theory which is
surprisingly simple and useful for computation while still containing enough
structure for proving interesting results. The class will begin with the
definition of K-theory, Chern classes, and the Chern character. Additional
topics may include the Hopf invariant 1 problem, the J-homomorphism,
Stiefel-Whitney classes and Pontrjagin classes, cobordism groups and the
construction of exotic spheres, and the Atiyah-Singer Index Theorem.
### Notes

This class uses many sources; I will be providing typed notes with citations.
### Homework

### Presentations

- Monday, November 13: Yun Liu: Clifford algebras
- Wednesday, November 15: Sujit Rao: Elementary Bott Periodicity
- Friday, November 17: Oliver Wang: Even periodic theories
- Monday, November 20: Shruthi Sridhar: Serre--Swan
- Monday, November 27: Elise McMahon: Equivariant K-theory I
- Wednesday, November 29: Brandon Shapiro: Equivariant K-theory II
- Friday, December 1: David Mehrle: Real K-theory