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

Weiping Zhang
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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.

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Weiping Zhang. 2003-04-18. Heat kernels and the index theorems on even and odd dimensional manifolds. https://arxiv.org/abs/math/0304269

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