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

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

2003-04-18

arxiv.org/abs/math/0304269v1

Proceedings of the ICM, Beijing 2002, vol. 2, 361--372

Mathematics

Differential Geometry

Scientific paper

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.

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