Topological Hochschild Homology and Higher Characteristics

TL;DR

This paper links the Reidemeister trace, a fixed point invariant, to topological Hochschild homology transfer, extending classical results and advancing understanding of fixed point invariants in algebraic topology.

Contribution

It establishes a novel connection between the Reidemeister trace and topological Hochschild homology transfer, broadening the theoretical framework in algebraic topology.

Findings

Reidemeister trace arises as a topological Hochschild homology transfer

Generalizes classical fixed point invariant results

Develops relationships between shadows, THH, and Morita invariance

Abstract

We show that an important classical fixed point invariant, the Reidemeister trace, arises as a topological Hochschild homology transfer. This generalizes a corresponding classical result for the Euler characteristic and is a first step in showing the Reidemeister trace is in the image of the cyclotomic trace. The main result follows from developing the relationship between shadows, topological Hochschild homology, and Morita invariance in bicategorical generality.