MATH 6530

K-Theory and Characteristic Classes

Course Description

Course information provided by the Courses of Study 2022-2023.

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.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: MATH 6510, or permission of instructor.

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