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

Félix, Yves; Murillo, Aniceto

doi:10.1090/S0002-9939-98-04192-6

A bound for the nilpotency of a group of self homotopy equivalences
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by Yves Félix and Aniceto Murillo PDF

Proc. Amer. Math. Soc. 126 (1998), 625-627 Request permission

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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