Nilpotency of self homotopy equivalences with coefficients

[Nilpotence des auto-équivalences d’homotopie avec des coefficients]

Cuvilliez, Maxence¹ ; Murillo, Aniceto²  ; Viruel, Antonio³

¹ Universidad de Málaga Departamento de Álgebra, Geometría y Topología Ap. 59, 29080 Málaga (Spain)
² Universidad de Málaga Departamento de Álgebra, Geometría y Topología Ap. 59, 29080 Málaga, SPAIN
³ Universidad de Málaga, Departamento de Álgebra, Geometría y Topología, Ap. 59, 29080 Málaga, SPAIN.

Annales de l'Institut Fourier, Tome 61 (2011) no. 1, pp. 351-364.

Abstract (VO)

In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.

Résumé

Nous étudions la nilpotence de certains groupes d’auto-équivalences d’homotopie. Notre objectif principal est d’étendre, aux groupes d’homotopy localisés et/ou aux groupes homotopie avec des coefficients, le principe général de Dror et A.  Zabrodsky par lequel un groupe d’auto-équivalences d’homotopie d’un complexe fini, qui agit de façon nilpotente sur les groupes homotopie, est lui-même nilpotent

Détail

DOI : 10.5802/aif.2604

Classification : 55P10
Keywords: Self homotopy equivalence
Mots-clés : auto équivalence d’homotopie

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