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 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 \mathrm {HNil}_\mathbb Q(\mathrm {aut}_1(X))\leqslant\mathrm {cocat}_\mathbb Q(\mathrm {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.
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