Related papers: Classifying Spaces with Virtually Cyclic Stabilise…

In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the…

By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality aleph-n admits a finite dimensional classifying space with virtually cyclic stabilizers of…

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 Bredon cohomological dimension of G for the families of…

We show that every discrete subgroup of $\mathrm{GL}(n,\mathbb{R})$ admits a finite dimensional classifying space with virtually cyclic stabilizers. Applying our methods to $\mathrm{SL}(3,\mathbb{Z})$, we obtain a four dimensional…

We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually…

By examining commensurators of virtually cyclic groups, we show that for each natural number n, any locally finite-by-virtually cyclic group of cardinality aleph_n admits a finite dimensional classifying space with virtually cyclic…

This is a revised version of the author's PhD thesis, including the corrections by the examiners. It also includes a few additional small corrections. In this thesis the objects of study are classifying spaces of groups with stabilisers in…

Given a group $G$ and a family of subgroups $\mathcal{F}$, we consider its classifying space $E_{\mathcal F}G$ with respect to $\mathcal{F}$. When $\mathcal F = \mathcal{VC}yc$ is the family of virtually cyclic subgroups, Juan-Pineda and…

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.

We are interested in the relationship between the virtual cohomological dimension (or vcd) of a discrete group Gamma and the smallest possible dimension of a model for the classifying space of Gamma relative to its family of virtually…

Let G be a discrete group which acts properly and isometrically on a complete CAT(0)-space X. Consider an integer d with d=1 or d greater or equal to 3 such that the topological dimension of X is bounded by d. We show the existence of a…

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups,…

We give a bound for the geometric dimension for the family of virtually cyclic groups in mapping class groups of a compact surface with punctures, possibly with nonempty boundary and negative Euler characteristic.

This thesis concerns the study of the Bredon cohomological and geometric dimensions of a discrete group $G$ with respect to a family $\mathfrak{F}$ of subgroups of $G$. With that purpose, we focus on building finite-dimensional models for…

For a group $G$ we consider the classifying space $E_{\mathcal{VC}yc}(G)$ for the family of virtually cyclic subgroups. We show that an Artin group admits a finite model for $E_{\mathcal{VC}yc}(G)$ if and only if it is virtually cyclic.…

We prove that, for $n\geq 3$, the minimal dimension of a model of the classifying space of the full braid group $B_n$, and of the pure braid group $P_n$, with respect to the family of virtually cyclic groups is $n$.

In this note we give an upper bound for the virtually cyclic dimension of any normally poly-free group in terms of its length. In particular, this implies that virtually even Artin groups of FC-type admit a finite dimensional model for the…

We determine the large scale geometry of the minimal displacement set of a hyperbolic isometry of a systolic complex. As a consequence, we describe the centraliser of such an isometry in a systolic group. Using these results, we construct a…

We construct groups G that are virtually torsion-free and have virtual cohomological dimension strictly less than the minimal dimension for any model for the classifying space for proper actions of G. They are the first examples that have…

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually…