## Publicacions Matemàtiques

### Intermediaries in Bredon (Co)homology and Classifying Spaces

#### Abstract

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.

#### Article information

Source
Publ. Mat., Volume 56, Number 2 (2012), 393-412.

Dates
First available in Project Euclid: 19 June 2012

https://projecteuclid.org/euclid.pm/1340127811

Mathematical Reviews number (MathSciNet)
MR2978329

Zentralblatt MATH identifier
1326.55007

Subjects
Primary: 20J05: Homological methods in group theory

#### Citation

Dembegioti, Fotini; Petrosyan, Nansen; Talelli, Olympia. Intermediaries in Bredon (Co)homology and Classifying Spaces. Publ. Mat. 56 (2012), no. 2, 393--412. https://projecteuclid.org/euclid.pm/1340127811

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