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.
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
Keywords: Self homotopy equivalence
Mot clés : auto équivalence d’homotopie
@article{AIF_2011__61_1_351_0, author = {Cuvilliez, Maxence and Murillo, Aniceto and Viruel, Antonio}, 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}, doi = {10.5802/aif.2604}, zbl = {1221.55008}, mrnumber = {2828133}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2604/} }
TY - JOUR AU - Cuvilliez, Maxence AU - Murillo, Aniceto AU - Viruel, Antonio TI - Nilpotency of self homotopy equivalences with coefficients JO - Annales de l'Institut Fourier PY - 2011 SP - 351 EP - 364 VL - 61 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2604/ DO - 10.5802/aif.2604 LA - en ID - AIF_2011__61_1_351_0 ER -
%0 Journal Article %A Cuvilliez, Maxence %A Murillo, Aniceto %A Viruel, Antonio %T Nilpotency of self homotopy equivalences with coefficients %J Annales de l'Institut Fourier %D 2011 %P 351-364 %V 61 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2604/ %R 10.5802/aif.2604 %G en %F AIF_2011__61_1_351_0
Cuvilliez, Maxence; Murillo, Aniceto; Viruel, Antonio. Nilpotency of self homotopy equivalences with coefficients. Annales de l'Institut Fourier, Volume 61 (2011) no. 1, pp. 351-364. doi : 10.5802/aif.2604. http://archive.numdam.org/articles/10.5802/aif.2604/
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