Open Access
2012 Intermediaries in Bredon (Co)homology and Classifying Spaces
Fotini Dembegioti, Nansen Petrosyan, Olympia Talelli
Publ. Mat. 56(2): 393-412 (2012).


For certain contractible $G$-CW-complexes and $\mathfrak F$ a family of subgroups of $G$, we construct a spectral sequence converging to the $\mathfrak F$-Bredon cohomology of $G$ with $\mathrm{E}_1$-terms given by the $\mathfrak F$-Bredon cohomology of the stabilizer subgroups. As applications, we obtain several corollaries concerning the cohomological and geometric dimensions of the classifying space $E_{\mathfrak {F}}G$. We also introduce, for any subgroup closed class of groups $\mathfrak F$, a hierarchically defined class of groups and show that if a group $G$ is in this class, then $G$ has finite $\mathfrak F\cap G$-Bredon (co)homological dimension if and only if $G$ has jump $\mathfrak F\cap G$-Bredon (co)homology.


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Fotini Dembegioti. Nansen Petrosyan. Olympia Talelli. "Intermediaries in Bredon (Co)homology and Classifying Spaces." Publ. Mat. 56 (2) 393 - 412, 2012.


Published: 2012
First available in Project Euclid: 19 June 2012

zbMATH: 1326.55007
MathSciNet: MR2978329

Primary: 20J05

Keywords: Bredon (co)homology , classifying space , spectral sequence

Rights: Copyright © 2012 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.56 • No. 2 • 2012
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