Geodesic
On the group of self-homotopy equivalences of a 2-connected and 6-dimensional CW-complex
Homology, homotopy, and applications, Tome 26 (2024) no. 1, pp. 151-168.

Voir la notice de l'article provenant de la source International Press of Boston

Let $X$ be a $2$-connected and $6$-dimensional CW‑complex such that $H_3 (X) \otimes \mathbb{Z}_2 = 0$. This paper aims to describe the group $\mathcal{E}(X)$ of the self-homotopy equivalences of $X$ modulo its normal subgroup $\mathcal{E}_\ast (X)$ of the elements that induce the identity on the homology groups. Making use of the Whitehead exact sequence of $X$, denoted by WES($X$), we define the group $\Gamma S(X)$ of $\Gamma$-automorphisms of WES($X$) and we prove that $\mathcal{E}(X)/\mathcal{E}_\ast (X) \cong \Gamma \mathcal{S}(X)$.
DOI : 10.4310/HHA.2024.v26.n1.a10
Classification : 55P10, 55P15
Keywords: Whitehead’s exact sequence, $\Gamma$-automorphism, group of self-homotopy equivalences 
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     title = {On the group of self-homotopy equivalences of a 2-connected and 6-dimensional {CW-complex}},
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Mahmoud Benkhalifa. On the group of self-homotopy equivalences of a 2-connected and 6-dimensional CW-complex. Homology, homotopy, and applications, Tome 26 (2024) no. 1, pp. 151-168. doi : 10.4310/HHA.2024.v26.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n1.a10/

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