Topological Hochschild homology and higher characteristics

Campbell, Jonathan; Ponto, Kate

doi:10.2140/agt.2019.19.965

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Topological Hochschild homology and higher characteristics

Jonathan A Campbell and Kate Ponto

Algebraic & Geometric Topology 19 (2019) 965–1017

DOI: 10.2140/agt.2019.19.965

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.

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/

Volume 19, issue 2 (2019)