An equivariant Lefschetz fixed-point formula for correspondences

TL;DR

This paper develops an equivariant Lefschetz fixed-point theorem for correspondences, providing multiple computational methods and extending classical fixed-point results to a broader equivariant setting.

Contribution

It introduces an equivariant Lefschetz fixed-point formula applicable to arbitrary correspondences, using geometric, algebraic, and trace-based approaches.

Findings

Derived an equivariant Lefschetz fixed-point formula

Connected geometric correspondences with algebraic localisation methods

Extended fixed-point theory to general equivariant correspondences

Abstract

We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using localisation, and as a Hattori-Stallings trace. This results in an equivariant version of the classical Lefschetz fixed-point theorem, which applies to arbitrary equivariant correspondences, not just maps.