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arXiv · 2507.01637

Free loop spaces and the Cauchy--Frobenius Lemma

Joachim Kock·Thomas Jan Mikhail
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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.

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Joachim Kock, Thomas Jan Mikhail. 2025-07-02. Free loop spaces and the Cauchy--Frobenius Lemma. https://arxiv.org/abs/2507.01637

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