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Nilpotency of self homotopy equivalences with coefficients

Maxence Cuvilliez, Aniceto Murillo, Antonio Viruel (2011)

Annales de l’institut Fourier

In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.

Nilpotent subgroups of the group of fibre homotopy equivalences.

Yves Félix, Jean-Claude Thomas (1995)

Publicacions Matemàtiques

Let ξ = (E, p, B, F) be a Hurewicz fibration. In this paper we study the space LG(ξ) consisting of fibre homotopy self equivalences of ξ inducing by restriction to the fibre a self homotopy equivalence of F belonging to the group G. We give in particular conditions implying that π1(LG(ξ)) is finitely generated or that L1(ξ) has the same rational homotopy type as aut1(F).

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