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Bibliographic Details
Main Author: Mayeda, Patrick
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.08907
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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