Related papers: CAT(0) groups with specified boundary

The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska. Our approach is to seek results analogous to those of Sela,…

We prove that if G is a discrete group that admits a metrically proper action on a finite-dimensional CAT(0) cube complex X, then G is weakly amenable. We do this by constructing uniformly bounded Hilbert space representations for which the…

This thesis is dedicated to random walks on spaces with non-positive curvature. In particular, we study the case of group actions on CAT(0) spaces that admit contracting elements, that is, whose properties mimic those of loxodromic…

This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological full groups). We determine that any piecewise full group that is locally compact in the compact-open topology…

Let $\Gamma$ be a finitely generated group of matrices over $\mathbb{C}$. We construct an isometric action of $\Gamma$ on a complete CAT(0) space $X$ such that the restriction of this action to any subgroup of $\Gamma$ containing no…

We study direct limits of embedded Cantor sets and embedded \sier curves. We show that under appropriate conditions on the embeddings, all limits of Cantor spaces give rise to homeomorphic spaces, called $\omega$-Cantor spaces, and…

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…

If G is a group acting properly by semisimple isometries on a proper CAT(0) space X, then we build models for the classifying spaces E_{vc} and E_{fbc} under the additional assumption that the action of G has a well-behaved collection of…

In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than one boundary. This contrasted with the situation for word hyperbolic groups, where it was well-known that each such group admitted a unique boundary---in a very…

In this short note, we show that a group acting geometrically on a CAT(0) cube complex with virtually abelian hyperplane-stabilisers must decompose virtually as a free product of free abelian groups and surface groups.

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.

Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…

The space of directions is a notion of boundary associated to an arbitrary totally disconnected locally compact group. We explicitly calculate the space of directions of a group acting vertex transitively with compact open vertex…

We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group $G$. In situations where these bounds conflict we obtain obstructions to $G$ being cocompactly cubulated. More…

We develop the boundary theory of rough CAT(0) spaces, a class of spaces that contains both Gromov hyperbolic and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic space and…

We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.

We give a classification and complete algebraic description of groups allowing only finitely many (left multiplication invariant) circular orders. In particular, they are all solvable groups with a specific semi-direct product…

Ballmann's Rank Rigidity Conjecture predicts that a CAT(0) space of higher rank with a geometric group action is rigid -- isometric to a Riemannian symmetric space, a Euclidean building, or splits as a direct product. We confirm this…

It is an open question whether right-angled Coxeter groups have unique group-equivariant visual boundaries. Croke and Kleiner present a right-angled Artin group with more than one visual boundary. In this paper we present a right-angled…