Our main purpose in this paper is to resolve, in a rational homotopy theory context, the following open question asked by S. Theriaul: given a topological space , what one may say about the nilpotency of aut when the cocategory of its classifying space Baut is finite? Here aut denotes the path component of the identity map in the set of self homotopy equivalences of . More precisely, we prove that
Publié le :
DOI : 10.4171/RSMUP/138-10
DOI : 10.4171/RSMUP/138-10
Classification :
55
Mots-clés : Rational homotopy theory, Sullivan minimal models, Quillen minimal models, self homotopy equivalences, classifying space, cocategory, homotopical nilpotency, Lie derivation
Mots-clés : Rational homotopy theory, Sullivan minimal models, Quillen minimal models, self homotopy equivalences, classifying space, cocategory, homotopical nilpotency, Lie derivation
Affiliations des auteurs :
Ben El Krafi, Badr 1 ;
Mamouni, My Ismail 2
@article{RSMUP_2017__138__209_0, author = {Ben El Krafi, Badr and Mamouni, My Ismail}, title = {On the {Theriault} conjecture for self homotopy equivalences}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {209--221}, publisher = {European Mathematical Society Publishing House}, address = {Zuerich, Switzerland}, volume = {138}, year = {2017}, doi = {10.4171/RSMUP/138-10}, mrnumber = {3743252}, zbl = {1383.55008}, url = {http://www.numdam.org/articles/10.4171/RSMUP/138-10/} }
TY - JOUR AU - Ben El Krafi, Badr AU - Mamouni, My Ismail TI - On the Theriault conjecture for self homotopy equivalences JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2017 SP - 209 EP - 221 VL - 138 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/138-10/ DO - 10.4171/RSMUP/138-10 ID - RSMUP_2017__138__209_0 ER -
%0 Journal Article %A Ben El Krafi, Badr %A Mamouni, My Ismail %T On the Theriault conjecture for self homotopy equivalences %J Rendiconti del Seminario Matematico della Università di Padova %D 2017 %P 209-221 %V 138 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/138-10/ %R 10.4171/RSMUP/138-10 %F RSMUP_2017__138__209_0
Ben El Krafi, Badr; Mamouni, My Ismail. On the Theriault conjecture for self homotopy equivalences. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 209-221. doi : 10.4171/RSMUP/138-10. http://www.numdam.org/articles/10.4171/RSMUP/138-10/
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