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
when is a simply connected CW-complex of finite type and that the equality holds when Baut is coformal. Many intersections with other popular open questions will be discussed.
Cite this article
Badr Ben El Krafi, My Ismail Mamouni, On the Theriault conjecture for self homotopy equivalences. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 209–221DOI 10.4171/RSMUP/138-10