The multiplicativity of fixed point invariants

TL;DR

This paper establishes formal factorization theorems for fixed-point invariants like Lefschetz number and Reidemeister trace in fibrations, enabling broader generalizations through bicategorical trace frameworks.

Contribution

It introduces general, formal factorization theorems for fixed-point invariants, extending multiplicativity results within an abstract bicategorical trace setting.

Findings

Proves factorization theorems for Lefschetz number and Reidemeister trace

Demonstrates multiplicativity of fixed-point invariants in fibrations

Framework allows easy generalizations to other contexts

Abstract

We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen numbers of a fibration. Moreover, the proofs of these theorems are essentially formal, taking place in the abstract context of bicategorical traces. This makes generalizations to other contexts straightforward.