Finite groups as homotopy self-equivalences of finite spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913707012915200 |
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| author | Celis-Rojas, Juan Felipe |
| author_facet | Celis-Rojas, Juan Felipe |
| contents | We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we present a new construction of a finite space whose group of homotopy classes of self-homotopy equivalences is isomorphic to $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite groups as homotopy self-equivalences of finite spaces Celis-Rojas, Juan Felipe Algebraic Topology We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we present a new construction of a finite space whose group of homotopy classes of self-homotopy equivalences is isomorphic to $G$. |
| title | Finite groups as homotopy self-equivalences of finite spaces |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2411.01005 |