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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08907 |
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| _version_ | 1866908647404077056 |
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| author | Mayeda, Patrick |
| author_facet | Mayeda, Patrick |
| contents | We prove a structural result concerning the exit path category associated to a manifold $M$ equipped with a smooth action of a finite group $G$. Specifically, the functor $Π: \mathsf{Exit}(M) \rightarrow \mathsf{Exit}(M/G)$ is a right fibration and $\mathsf{Enter}(M/G)$ is classified by a natural functor $\mathsf{Enter}(M/G) \rightarrow O_G$, where $O_G$ is the orbit category of $G$. The main technical result manipulates exit paths to immediately exiting paths, enabling lifts of homotopies in $M/G$ to homotopies in $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exit path categories induced by group actions Mayeda, Patrick Algebraic Topology (2020) 55P91, 57N80, 18N60, 18F20, 55R05 We prove a structural result concerning the exit path category associated to a manifold $M$ equipped with a smooth action of a finite group $G$. Specifically, the functor $Π: \mathsf{Exit}(M) \rightarrow \mathsf{Exit}(M/G)$ is a right fibration and $\mathsf{Enter}(M/G)$ is classified by a natural functor $\mathsf{Enter}(M/G) \rightarrow O_G$, where $O_G$ is the orbit category of $G$. The main technical result manipulates exit paths to immediately exiting paths, enabling lifts of homotopies in $M/G$ to homotopies in $M$. |
| title | Exit path categories induced by group actions |
| topic | Algebraic Topology (2020) 55P91, 57N80, 18N60, 18F20, 55R05 |
| url | https://arxiv.org/abs/2511.08907 |