Displaying 181 – 200 of 268

Showing per page

Self homotopy equivalences of classifying spaces of compact connected Lie groups

Stefan Jackowski, James McClure, Bob Oliver (1995)

Fundamenta Mathematicae

We describe, for any compact connected Lie group G and any prime p, the monoid of self maps B G p B G p which are rational equivalences. Here, B G p denotes the p-adic completion of the classifying space of G. Among other things, we show that two such maps are homotopic if and only if they induce the same homomorphism in rational cohomology, if and only if their restrictions to the classifying space of the maximal torus of G are homotopic.

Spaces associated to quadratic endofunctors of the category of groups.

Hans-Joachim Baues, Teimuraz Pirashvili (2005)

Extracta Mathematicae

Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π2(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.

Currently displaying 181 – 200 of 268