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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2011-04
Main Authors: Dembegioti, Fotini, Petrosyan, Nansen, Talelli, Olympia
Format: Article
Language:English
Subjects:
Classification
Homology
Subgroups
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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 for the family F. We also introduce a hierarchically defined class of groups which contains all countable elementary amenable groups and countable linear groups of characteristic zero, and show that if a group G is in this class, then G has finite F-Bredon (co)homological dimension if and only if G has jump F-Bredon (co)homology.
ISSN:2331-8422