Title: Genera of manifolds in K-theory
Speaker: Takuo Matsuoka
Speaker Info: Northwestern University
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.Date: Thursday, January 27, 2011
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.