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Topological Hochschild homology and higher characteristics

Jonathan A Campbell and Kate Ponto

Algebraic & Geometric Topology 19 (2019) 965–1017
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 (see Astérisque 333, Soc. Math. France, Paris (2010)), topological Hochschild homology and Morita-invariance in bicategorical generality.

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Keywords
topological Hochschild homology, Reidemeister trace, Morita equivalence, bicategorical trace
Mathematical Subject Classification 2010
Primary: 16D90, 19D55, 55R12
Secondary: 18D05, 55M20
References
Publication
Received: 13 March 2018
Revised: 30 August 2018
Accepted: 19 September 2018
Published: 12 March 2019
Authors
Jonathan A Campbell
Department of Mathematics
Vanderbilt University
Nashville, TN
United States
http://www.jonathanacampbell.com
Kate Ponto
Department of Mathematics
University of Kentucky
Lexington, KY
United States
http://www.ms.uky.edu/~kate/