A Semiclassical Heat Kernel Proof of the Poincaré-Hopf Theorem

Abstract

We treat the Witten operator on the de Rham complex with semiclassical heat kernel methods to derive the Poincaré-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.

27 pages

References in corpus (2)

• Asymptotic heat kernel expansion in the semi-classical limit
• Vector Fields with a non-degenerate Source