Equivariant Fixed Point Theory

TL;DR

This paper revisits equivariant fixed point invariants like the Lefschetz number and Reidemeister trace, providing clearer, categorical descriptions and comparisons to prior definitions, highlighting their algebraic properties.

Contribution

It introduces a categorical trace approach to equivariant fixed point invariants, simplifying their conceptual understanding and comparison to existing generalizations.

Findings

Categorical trace provides simple descriptions of invariants.

Clear comparisons between new and previous definitions.

Highlights additivity and multiplicativity properties.

Abstract

We reexamine equivariant generalizations of the Lefschetz number and Reidemeister trace using categorical traces. This gives simple, conceptual descriptions of the invariants as well as direct comparisons to previously defined generalizations. These comparisons are illuminating applications of the additivity and multiplicativity of the categorical trace.