Displaying similar documents to “Restoration of structure”

Nilpotent subgroups of the group of fibre homotopy equivalences.

Yves Félix, Jean-Claude Thomas (1995)

Publicacions Matemàtiques

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Let ξ = (E, p, B, F) be a Hurewicz fibration. In this paper we study the space L(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 π(L(ξ)) is finitely generated or that L(ξ) has the same rational homotopy type as aut(F).

Miller spaces and spherical resolvability of finite complexes

Jeffrey Strom (2003)

Fundamenta Mathematicae

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Let 𝒜 be a fixed collection of spaces, and suppose K is a nilpotent space that can be built from spaces in 𝒜 by a succession of cofiber sequences. We show that, under mild conditions on the collection 𝒜, it is possible to construct K from spaces in 𝒜 using, instead, homotopy (inverse) limits and extensions by fibrations. One consequence is that if K is a nilpotent finite complex, then ΩK can be built from finite wedges of spheres using homotopy limits and extensions by fibrations....

Nilpotency of self homotopy equivalences with coefficients

Maxence Cuvilliez, Aniceto Murillo, Antonio Viruel (2011)

Annales de l’institut Fourier

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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.