Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Yves Félix; Aniceto Murillo
Journal: Proc. Amer. Math. Soc. 126 (1998), 625-627.
MSC (1991): Primary 55P10, 55M30
MathSciNet review: 1443152
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Abstract: Let $\mathcal{E}_\Omega(X)$ be the group of homotopy classes of self-homotopy equivalences of $X$ 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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