author={Fotini Dembegioti and Nansen Petrosyan and Olympia Talelli},
  journal={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
Bredon cohomology and its applications to hierarchically defined groups B
By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class LHFF of type Bredon-FP∞ admits a finite dimensional model for EFG. We also show thatExpand
Bredon cohomological dimensions for groups acting on CAT(0)-spaces
Let G be a group acting isometrically with discrete orbits on a separable complete CAT(0)-space of bounded topological dimension. Under certain conditions, we give upper bounds for the BredonExpand
Cohomological and geometric invariants of simple complexes of groups
We investigate strictly developable simple complexes of groups with arbitrary local groups, or equivalently, group actions admitting a strict fundamental domain. We introduce a new method forExpand
Complete Bredon cohomology and its applications to hierarchically defined groups
Abstract By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class $\cll\clh^{\mathfrak F}{\mathfrak F}$ of type Bredon-FP∞ admits a finiteExpand
Bredon cohomological dimensions for proper actions and Mackey functors
For groups with a uniform bound on the length of chains of finite subgroups, we study the relationship between the Bredon cohomological dimension for proper actions and the notions of cohomologicalExpand
Some 1-groups with unbounded torsion and a conjecture of Kropholler and Mislin
Kropholler and Mislin conjectured that groups acting admissibly on a finite-dimensional G-CW-complex with finite stabilisers admit a finite-dimensional model for E_FG, the classifying space forExpand
Geometric dimension of groups for the family of virtually cyclic subgroups
By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality ℵ n admits a finite‐dimensional classifying space withExpand
Dimension invariants of outer automorphism groups
The geometric dimension for proper actions $\underline{\mathrm{gd}}(G)$ of a group $G$ is the minimal dimension of a classifying space for proper actions $\underline{E}G$. We construct for everyExpand
A cohomological characterization of locally virtually cyclic groups
We show that a countable group is locally virtually cyclic if and only if its Bredon cohomological dimension for the family of virtually cyclic subgroups is at most one.
On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups
We show that elementary amenable groups, which have a bound on the orders of their finite subgroups, admit a finite dimensional model for the classifying space with virtually cyclic isotropy.


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
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
  • J. Jo, B. Nucinkis
  • 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.
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