Free loop spaces and the Cauchy--Frobenius Lemma
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913922808807424 |
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| author | Kock, Joachim Mikhail, Thomas Jan |
| author_facet | Kock, Joachim Mikhail, Thomas Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free loop spaces and the Cauchy--Frobenius Lemma Kock, Joachim Mikhail, Thomas Jan Algebraic Topology Category Theory Group Theory 20-XX, 58D19, 55P35, 18N60 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. |
| title | Free loop spaces and the Cauchy--Frobenius Lemma |
| topic | Algebraic Topology Category Theory Group Theory 20-XX, 58D19, 55P35, 18N60 |
| url | https://arxiv.org/abs/2507.01637 |