MATH 6530 - [K-Theory and Characteristic Classes]

Fall. Not offered: 2021-2022. Next offered: 2022-2023. 4 credits. Student option grading.

Prerequisite: MATH 6510, or permission of instructor.

Staff.

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.