Intermediaries in Bredon (co)homology and classifying spaces

For certain contractible G-CW-complexes and F a family of subgroups of G, we construct a spectral sequence converging to the F-Bredon cohomology of G with E1-terms given by the F-Bredon cohomology of the stabilizer subgroups. As applications, we obtain several corollaries concerning the cohomologica...

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Bibliographic Details
Published in:Publicacions matemàtiques 2012, Vol.56 (2), p.393-412
Main Authors: Dembegioti, F., Petrosyan, N., Talelli, O.
Format: Article
Language:English
Subjects:
20J05
Algebra
Bredon (co)homology
Classifying space
Functors
Integers
Isotropy
Jumping
Mathematical manifolds
Mathematical theorems
Mathematics
Morphisms
spectral sequence
Vertices
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Summary:For certain contractible G-CW-complexes and F a family of subgroups of G, we construct a spectral sequence converging to the F-Bredon cohomology of G with E1-terms given by the F-Bredon cohomology of the stabilizer subgroups. As applications, we obtain several corollaries concerning the cohomological and geometric dimensions of the classifying space EFG. We also introduce, for any subgroup closed class of groups F, a hierarchically de ned class of groups and show that if a group G is in this class, then G has finite F ∩ G-Bredon (co)homological dimension if and only if G has jump F ∩ G-Bredon (co)homology.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_56212_06