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An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary

Xianzhe Dai·Weiping Zhang
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Abstract

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of $η$ type associated to $K^1$ representatives on even dimensional manifolds, which should be of independent interests. For example, it gives an intrinsic interpretation of the so called Wess-Zumino term in the WZW theory in physics.

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BibTeXRIS

Xianzhe Dai, Weiping Zhang. 2006-05-06. An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary. https://arxiv.org/abs/math/0103230

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