TY  - JOUR
A1  - Ludewig, Matthias
T1  - A semiclassical heat kernel proof of the Poincare-Hopf theorem
T2  - Manuscripta mathematica
N2  - 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.
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/38619
SN  - 0025-2611
SN  - 1432-1785
VL  - 148
IS  - 1-2
SP  - 29
EP  - 58
PB  - Springer
CY  - Heidelberg
ER  -