Nilpotency of self homotopy equivalences with coefficients

Cuvilliez, Maxence; Murillo, Aniceto; Viruel, Antonio

doi:10.5802/aif.2604

Nilpotency of self homotopy equivalences with coefficients
[Nilpotence des auto-équivalences d’homotopie avec des coefficients]

Cuvilliez, Maxence ¹ ; Murillo, Aniceto ² ; Viruel, Antonio ³

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.

Résumé
Abstract

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

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.

MR Zbl

DOI : 10.5802/aif.2604

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

Affiliations des auteurs :

Cuvilliez, Maxence ¹ ; Murillo, Aniceto ² ; Viruel, Antonio ³

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     title = {Nilpotency of self homotopy equivalences with coefficients},
     journal = {Annales de l'Institut Fourier},
     pages = {351--364},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {1},
     year = {2011},
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     zbl = {1221.55008},
     mrnumber = {2828133},
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     url = {http://www.numdam.org/articles/10.5802/aif.2604/}
}

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Cuvilliez, Maxence; Murillo, Aniceto; Viruel, Antonio. Nilpotency of self homotopy equivalences with coefficients. Annales de l'Institut Fourier, Tome 61 (2011) no. 1, pp. 351-364. doi : 10.5802/aif.2604. http://www.numdam.org/articles/10.5802/aif.2604/

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