On the Theriault conjecture for self homotopy equivalences
Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 209-221.

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 X, what one may say about the nilpotency of aut 1 (X) when the cocategory of its classifying space Baut 1 (X) is finite? Here aut 1 (X) denotes the path component of the identity map in the set of self homotopy equivalences of X. More precisely, we prove that

HNil ( aut 1 (X)) cocat ( Baut 1 (X)),
when X is a simply connected CW-complex of finite type and that the equality holds when Baut 1 (X) is coformal. Many intersections with other popular open questions will be discussed.

Publié le :
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
Ben El Krafi, Badr 1 ; Mamouni, My Ismail 2

1 Hassan II University Aïn Chock, Casablanca, Morocco
2 CRMEF Rabat, Morocco
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     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/}
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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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