Heat kernels and the index theorems on even and odd dimensional manifolds

Abstract

In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss the odd dimensional counterparts of the above results. In particular, we describe a joint result with Xianzhe Dai on an index theorem for Toeplitz operators on odd dimensional manifolds with boundary.

References in corpus (1)

• The eta-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary

Cited by in corpus (4)

• Eta Invariants for Even Dimensional Manifolds
• Heat kernel coefficients on Kahler manifolds
• An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary
• Eta invariant and holonomy, the even dimensional case