1. On the Theriault conjecture for self homotopy equivalences.
- Author
-
EL KRAFI, BADR BEN and MAMOUNI, MY ISMAIL
- Subjects
HOMOTOPY theory ,MINIMAL submanifolds ,NILPOTENT groups ,LIE algebras ,TOPOLOGICAL spaces ,INVARIANTS (Mathematics) - Abstract
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 aut1.(X) when the cocategory of its classifying space Baut1.(X) is finite? Here aut1.(X) denotes the path component of the identity map in the set of self homotopy equivalences of X. More precisely, we prove that HnilQ.aut1.(X) 6 cocatQ.Baut1.(X); when X is a simply connected CW-complex of finite type and that the equality holds when Baut1.(X) is coformal.Many intersections with other popular open questions will be discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF