Moscow Mathematical Journal

Volume 25, Issue 1, January–March 2025 pp. 1–12.

Torsion in the Group of Self-Homotopy Equivalences of a CW-Complex

Authors: Mahmoud Benkhalifa (1)
Author institution:(1) Department of Mathematics. College of Sciences, University of Sharjah, UAE

Summary:

Let $X$ be a simply connected CW-complex of dimension $n$ . This paper aims to establish a link between the groups $\mathcal{E}(X)$ and $\Gamma_n(X)$ . Here, $\mathcal{E}(X)$ represents the group of self-homotopy equivalences of $X$ , while the group $\Gamma_n(X)$ , which was intruduced by Whitehead, is the image of $\pi_n$ of the $(n-1)$ -skeleton of $X$ in $\pi_n$ of the $n$ -skeleton of $X$ . This pursuit provides significant insights into discerning the presence of torsion elements within $\mathcal{E}(X)$ .

2020 Math. Subj. Class. 55P10.

Keywords: Whitehead’s exact sequence, group of self-homotopy equivalences.

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