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A bound for the nilpotency of a group of self homotopy equivalences

Authors:	Yves Fé lix Aniceto Murillo

Institution:	Départment de Mathématiques, Université Catholique de Louvain, 1348 Louvain La, Neuve, Belgium ; Departamento de Algebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080-Málaga, Spain

Abstract:	Let $\mathcal{E}_\Omega(X)$ be the group of homotopy classes of self-homotopy equivalences of such that $\Omega f\simeq 1d_{\Omega X}$ . We prove that $\mathcal{E}_\Omega(X)$ is a nilpotent group and that $\operatorname{nil} \mathcal{E}_{\Omega}(X)\le \operatorname{cat}(X)-1$ .

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