Free loop spaces and the Cauchy-Frobenius Lemma

Proceedings of the American Mathematical Society 2026 Open access

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Authors: Joachim Kock, Thomas Jan Mikhail
DOI: 10.1090/proc/17905
Cited by: 0

Abstract

We upgrade the Cauchy--Frobenius Lemma (`Burnside's Lemma') to a homotopy equivalence of $\infty$-groupoids, essentially given by double counting/Fubini in the free loop space of the quotient.

Fields of Study & Subjects

Homotopy and Cohomology in Algebraic Topology Mathematics and Applications Advanced Topology and Set Theory

Publication details

Journal / source
Proceedings of the American Mathematical Society
Publication date
7 September 2026
Language
EN