Iterated traces in 2–categories and Lefschetz theorems

Campbell, Jonathan A; Ponto, Kate

doi:10.2140/agt.2022.22.815

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Iterated traces in $2$–categories and Lefschetz theorems

Jonathan A Campbell and Kate Ponto

Algebraic & Geometric Topology 22 (2022) 815–879

DOI: 10.2140/agt.2022.22.815

Abstract

While not obvious from its initial motivation in linear algebra, there are many contexts where iterated traces can be defined. We prove a very general theorem about iterated $2$ –categorical traces. We show that many Lefschetz-type theorems in the literature are consequences of this result and the new perspective we provide allows for immediate spectral generalizations.

Keywords

2-categories, Lefschetz theorems, traces, duality, iterated traces, Hochschild homology, monoidal bicategory

Mathematical Subject Classification

Primary: 18N10, 19K14, 37C25

References

Publication

Received: 22 July 2020

Revised: 27 October 2020

Accepted: 19 November 2020

Published: 3 August 2022

Authors

Jonathan A Campbell
Center for Communications Research, La Jolla San Diego, CA United States

Kate Ponto
Department of Mathematics University of Kentucky Lexington, KY United States

Volume 22, issue 2 (2022)