Maps between classifying spaces and applications
نویسندگان
چکیده
منابع مشابه
Maps between Classifying Spaces
In 1976, Adams & Mahmud 3] published the rst systematic study of the problem of determining the homological properties of maps between classifying spaces of compact connected Lie groups. This was continued in later work by one or both authors: Adams 2] extended some of the results to the case of non-connected Lie groups by using complex K-theory; while Adams & Mahmud 4] identiied further restri...
متن کاملMaps between classifying spaces revisited
In an earlier paper, we developed general techniques which can be used to study the set of homotopy classes of maps between the classifying spaces of two given compact Lie groups. Here, we describe more precisely the general strategy for doing this; and then, as a test of these methods, apply them to determine the existence and uniqueness of (potential) maps BG −→ BG′ studied earlier by Adams a...
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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 کاملRational equivalences between classifying spaces
The paper contains a homotopy classification of rational equivalences between classifying spaces of compact connected Lie groups with an application to genus sets of such spaces. Mathematics Subject Classification (1991): 55R35, 55P10, 55P60, 55S37
متن کاملSelf-maps of Classifying Spaces of Compact Simple Lie Groups
We describe here the set [BG, BG] of homotopy classes of self-maps of the classifying space BG , for any compact connected simple Lie group G. In particular, we show that two maps ƒ , f : BG —• BG are homotopic if and only if they are homotopic after restricting to the maximal torus of G ; or equivalently if and only if they induce the same homomorphism in rational cohomology. In addition, we i...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1993
ISSN: 0022-4049
DOI: 10.1016/0022-4049(93)90057-z