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arXiv · 1302.6895

A Semiclassical Heat Kernel Proof of the Poincar\'e-Hopf Theorem

Matthias Ludewig
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Abstract

We treat the Witten operator on the de Rham complex with semiclassical heat kernel methods to derive the Poincar\'e-Hopf theorem and degenerate generalizations of it. Thereby, we see how the semiclassical asymptotics of the Witten heat kernel are related to approaches using the Thom form of Mathai and Quillen.

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Matthias Ludewig. 2013-02-27. A Semiclassical Heat Kernel Proof of the Poincar\'e-Hopf Theorem. https://doi.org/10.1007/s00229-015-0741-y

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