Free loop spaces and the Cauchy--Frobenius Lemma
Algebraic Topology
2025-07-03 v1 Category Theory
Group Theory
Abstract
We upgrade the Cauchy--Frobenius Lemma (`Burnside's Lemma') to a homotopy equivalence of -groupoids, essentially given by double counting/Fubini in the free loop space of the quotient.
Keywords
Cite
@article{arxiv.2507.01637,
title = {Free loop spaces and the Cauchy--Frobenius Lemma},
author = {Joachim Kock and Thomas Jan Mikhail},
journal= {arXiv preprint arXiv:2507.01637},
year = {2025}
}
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4 pages