**Title:** Genera of manifolds in K-theory

**Speaker:** Takuo Matsuoka

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

A genus is a certain kind of cobordism invariant of manifolds whose values are 'numbers'. For spin manifolds, there is one called A-hat genus, whose values are integers (mod 2 in some context). This genus has an important meaning to topological K-theory.Even though A-hat genus has a simple description in terms of algebraic topology, the Atiyah--Singer index theorem can be used to give it an analytical meaning by describing it as the Fredholm index of a certain differential operator. I would like to explain this after giving a K-theoretic formulation of a version of the Atiyah--Singer theorem.

In the talk, I will review the definitions of topological K-theory, spin groups and spin manifolds, for the convenience of those who missed Jesse's talk in the fall.

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