Equivariant Lefschetz formulae and heat asymptotics

TL;DR

This paper establishes an equivariant Lefschetz formula for elliptic complexes on compact manifolds with symmetry, using heat equation techniques to connect geometric and topological invariants.

Contribution

It introduces a novel heat equation approach to derive equivariant Lefschetz formulas for elliptic complexes under Lie group actions.

Findings

Derived explicit formulas linking fixed points and heat kernel asymptotics.

Extended Lefschetz fixed point theory to equivariant elliptic complexes.

Provided new tools for analyzing symmetry in geometric analysis.

Abstract

We prove an equivariant Lefschetz formula for elliptic complexes over a compact manifold carrying the action of a compact Lie group of isometries via heat equation methods.