Equivariant Lefschetz number of differential operators

TL;DR

This paper establishes a trace density formula for the G-Lefschetz number of differential operators on compact complex manifolds with a compact Lie group action, extending previous results to orbifolds.

Contribution

It generalizes the trace density formula for G-Lefschetz numbers to orbifolds, broadening the scope of previous work on differential operators and group actions.

Findings

Derived a trace density formula for G-Lefschetz numbers on orbifolds

Extended previous results from manifolds to orbifolds

Provided a theoretical framework for equivariant Lefschetz numbers

Abstract

Let $G$ be a compact Lie group acting on a compact complex manifold $M$. We prove a trace density formula for the $G$-Lefschetz number of a differential operator on $M$. We generalize Engeli and Felder's recent results to orbifolds.