Geodesic
Every group is the group of self-homotopy equivalences of finite dimensional $\mathrm{CW}$-complex
Sbornik. Mathematics, Tome 215 (2024) no. 9, pp. 1182-1201

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We prove that any group $G$ occurs as $\mathcal{E}(X)$, where $X$ is a $\mathrm{CW}$-complex of finite dimension and $\mathcal{E}(X)$ denotes its group of self-homotopy equivalences. Thus, we generalize a well-known theorem due to Costoya and Viruel [9] asserting that any finite group occurs as $\mathcal{E}(X)$, where $X$ is rational elliptic space. Bibliography: 12 titles.
Keywords: Kahn's realisability problem of groups, group of homotopy self-equivalences, Anick's $R$-local homotopy theory. 
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     author = {M. Benkhalifa},
     title = {Every group is the group of self-homotopy equivalences of finite dimensional $\mathrm{CW}$-complex},
     journal = {Sbornik. Mathematics},
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     number = {9},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_9_a2/}
}
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M. Benkhalifa. Every group is the group of self-homotopy equivalences of finite dimensional $\mathrm{CW}$-complex. Sbornik. Mathematics, Tome 215 (2024) no. 9, pp. 1182-1201. http://geodesic.mathdoc.fr/item/SM_2024_215_9_a2/