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

Authors
  • Ludewig, Matthias
Type
Preprint
Publication Date
Sep 05, 2014
Submission Date
Feb 27, 2013
Identifiers
arXiv ID: 1302.6895
Source
arXiv
License
Yellow
External links

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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