Every group is the group of self homotopy equivalences of finite dimensional CW-complex
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916624976576512 |
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| author | Benkhalifa, Mahmoud |
| author_facet | Benkhalifa, Mahmoud |
| contents | We prove that any group $G$ occurs as $\E(X)$, where $X$ is CW-complex of finite dimension and $\E(X)$ denotes its group of self-homotopy equivalence. Thus, we generalize a well know-theorem due to Costoya and Viruel \cite{CV} asserting that any finite group occurs as $\E(X)$, where $X$ is rational elliptic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_13888 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Every group is the group of self homotopy equivalences of finite dimensional CW-complex Benkhalifa, Mahmoud Algebraic Topology We prove that any group $G$ occurs as $\E(X)$, where $X$ is CW-complex of finite dimension and $\E(X)$ denotes its group of self-homotopy equivalence. Thus, we generalize a well know-theorem due to Costoya and Viruel \cite{CV} asserting that any finite group occurs as $\E(X)$, where $X$ is rational elliptic space. |
| title | Every group is the group of self homotopy equivalences of finite dimensional CW-complex |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2110.13888 |