A semiclassical heat kernel proof of the Poincare-Hopf theorem
- We consider the semiclassical asymptotic expansion of the heat kernel coming from Witten's perturbation of the de Rham complex by a given function. For the index, one obtains a time-dependent integral formula which is evaluated by the method of stationary phase to derive the Poincare-Hopf theorem. We show how this method is related to approaches using the Thom form of Mathai and Quillen. Afterwards, we use a more general version of the stationary phase approximation in the case that the perturbing function has critical submanifolds to derive a degenerate version of the Poincare-Hopf theorem.
Author details: | Matthias Ludewig |
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DOI: | https://doi.org/10.1007/s00229-015-0741-y |
ISSN: | 0025-2611 |
ISSN: | 1432-1785 |
Title of parent work (English): | Manuscripta mathematica |
Publisher: | Springer |
Place of publishing: | Heidelberg |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Volume: | 148 |
Issue: | 1-2 |
Number of pages: | 30 |
First page: | 29 |
Last Page: | 58 |
Funding institution: | Potsdam Graduate School; Fulbright Commission |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |