Spaces of Maps into Classifying Spaces for Equivariant Crossed Complexes, II: The General Topological Group Case
نویسندگان
چکیده
The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coherence. Again, our results give information not just on the homotopy classification of certain equivariant maps, but also on the weak equivariant homotopy type of the corresponding equivariant function spaces. Mathematics Subject Classifications (2001): 55P91, 55U10, 18G55.
منابع مشابه
A ug 1 99 8 Spaces of maps into classifying spaces for equivariant crossed complexes , II : The general topological group case
Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case. Abstract The results of a previous paper [3] on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for cross...
متن کاملSpaces of maps into classifying spaces for equivariant crossed complexes
We give an equivariant version of the homotopy theory of crossed complexes. The applications generalize work on equivariant Eilenberg-Mac Lane spaces, including the non abelian case of dimension 1, and on local systems. It also generalizes the theory of equivariant 2-types, due to Moerdijk and Svensson. Further, we give results not just on the homotopy classification of maps but also on the hom...
متن کاملHomotopy Theory of Lie groups and their Classifying Spaces
1. Lie groups, homomorphisms and linear representations. Irreducible representations. 2. Maximal tori in compact Lie groups. 3. Characters of representations. Ring of virtual characters. The Weyl theorem. 4. Actions of Lie groups. Homogeneous spaces (orbits) and equivariant maps. 5. Classifying spaces of topological groups and maps induced by homomorphisms. 6. Homotopy classification of maps be...
متن کاملExact Sequences of Fibrations of Crossed Complexes, Homotopy Classification of Maps, and Nonabelian Extensions of Groups
The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW -complex to the classifying space of a crossed module and also, ...
متن کاملHomotopy Actions by Topological Actions . Ii
A homotopy action of a group G on a space X is a homomorphism from G to the group HAUT(X) of homotopy classes of homotopy equivalences of X. George Cooke developed an 'obstruction theory to determine if a homotopy action is equivalent up to homotopy to a topological action. The question studied in this paper is: Given a diagram of spaces with homotopy actions of G and maps between them that are...
متن کامل