Intermediaries in Bredon (Co)homology and Classifying Spaces
Abstract
For certain contractible GCWcomplexes and F a family of subgroups of G, we construct a spectral sequence converging to the FBredon cohomology of G with E1terms given by the FBredon 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 FBredon (co)homological dimension if and only if G has jump FBredon (co)homology.
 Publication:

arXiv eprints
 Pub Date:
 April 2011
 arXiv:
 arXiv:1104.2539
 Bibcode:
 2011arXiv1104.2539D
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 Mathematics  Group Theory;
 18G60;
 55R35
 EPrint:
 18 pages