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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Yves Félix and 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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Additional Information

Yves Félix
Affiliation: Départment de Mathématiques, Université Catholique de Louvain, 1348 Louvain La, Neuve, Belgium
Email: felix@agel.ucl.ac.be

Aniceto Murillo
Affiliation: Departamento de Algebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080-Málaga, Spain
Email: aniceto@agt.cie.uma.es

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04192-6
PII: S 0002-9939(98)04192-6
Received by editor(s): August 19, 1996
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society