Iterated traces in 2–categories and Lefschetz theorems

Campbell, Jonathan A; Ponto, Kate

doi:10.2140/agt.2022.22.815

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

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)