Volume 22, issue 2 (2022)

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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

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.

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2-categories, Lefschetz theorems, traces, duality, iterated traces, Hochschild homology, monoidal bicategory
Mathematical Subject Classification
Primary: 18N10, 19K14, 37C25
Received: 22 July 2020
Revised: 27 October 2020
Accepted: 19 November 2020
Published: 3 August 2022
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