# INTERMEDIARIES IN BREDON (CO)HOMOLOGY AND CLASSIFYING SPACES

@article{Dembegioti2011INTERMEDIARIESIB,
title={INTERMEDIARIES IN BREDON (CO)HOMOLOGY AND CLASSIFYING SPACES},
author={Fotini Dembegioti and Nansen Petrosyan and Olympia Talelli},
journal={Publicacions Matematiques},
year={2011},
volume={56},
pages={393-412}
}
• Published 2011
• Mathematics
• Publicacions Matematiques
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… Expand
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#### References

SHOWING 1-10 OF 33 REFERENCES
On Bredon (co-)homological dimensions of groups
The objects of interest in this thesis are classifying spaces EFG for discrete groups G with stabilisers in a given family F of subgroups of G. The main focus of this thesis lies in the family Fvc(G)Expand
A spectral sequence in Bredon (co)homology
Abstract We construct a spectral sequence which relates the Bredon (co)homology groups of a group G with respect to two different families of subgroups of G satisfying certain restrictions. ThisExpand
Cohomological Finiteness Conditions in Bredon Cohomology
• Mathematics
• 2009
We show that any soluble group $G$ of type Bredon-$\FP_{\infty}$ with respect to the family of all virtually cyclic subgroups such that centralizers of infinite order elements are of typeExpand
Jumps in cohomology and free group actions
A discrete group G has periodic cohomology over R if there is an element in a cohomology group cup product with which it induces an isomorphism in cohomology after a certain dimension. Adem and SmithExpand
Periodic cohomology and subgroups with bounded Bredon cohomological dimension
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
• 2008
Abstract Mislin and Talelli showed that a torsion-free group in $\HF$ with periodic cohomology after some steps has finite cohomological dimension. In this note we look at similar questions forExpand
Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory.
• Mathematics
• 1998
We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory ofExpand
A characterization of cohomological dimension for a big class of groups
Abstract It was shown by Cornick and Kropholler (1998) in [5] that if a group G is in h F then the finitistic dimension of Z G , findim Z G , is equal to the supremum of the projective dimensions ofExpand
On groups of type (FP)
Let G be a group. A ZG-module M is said to be of type (FP)? over G if and only if there is a projective resolution P? ?M in which every Pi is finitely generated. We show that if G belongs to a largeExpand
On dimensions in Bredon homology
We define a homological and cohomological dimension of groups in the context of Bredon homology and compare the two quantities. We apply this to describe the Bredon-homological dimension of nilpotentExpand
The type of the classifying space for a family of subgroups
Abstract The classifying space E(Γ, F ) for a family F of subgroups of a group Γ is defined up to Γ -homotopy as a Γ - CW -complex E(Γ, F ) such that E(Γ, F ) H is contractible if H belongs to F andExpand