Related papers: Residually finite non linear hyperbolic groups

Given a finitely presented group $Q,$ we produce a short exact sequence $1\to N \hookrightarrow G \twoheadrightarrow Q \to 1$ such that $G$ is a torsion-free Gromov hyperbolic group without the unique product property and $N$ is without the…

Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. The Milnor-Schwarz lemma implies that groups with a common model geometry are quasi-isometric; however, the…

We study to what extent torsion-free (Gromov)-hyperbolic groups are elementarily equivalent to their finite index subgroups. In particular, we prove that a hyperbolic limit group either is a free product of cyclic groups and surface groups,…

In this paper we extend the construction of special representations to Gromov hyperbolic groups which admits complementary series. We prove that these representations have a natural non-trivial reduced cohomology class $[c]$. An analogue of…

We prove that every {finitely generated residually finite}-by-sofic group satisfies Kaplansky's direct and stable finiteness conjectures with respect to all noetherian rings. We use this result to provide countably many new examples of…

We begin the investigation of Gamma-limit groups, where Gamma is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of Drutu and Sapir, we adapt the results from math.GR/0404440 to…

We discuss the linearity and discreteness of amalgamated products of linear word-hyperbolic groups. In particular, we prove that the double of an Anosov group along a maximal cyclic subgroup is always linear, and we construct examples of…

We prove that amongst the class of free-by-cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever $G$ is a free-by-cyclic group with first Betti number equal to one, and $H$ is a…

In this paper we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties. We give the first examples of subgroups of hyperbolic groups which are of type $FP_2$ but not finitely presented. We…

We give examples of hyperbolic groups with finite-rank free subgroups of huge (Ackermannian) distortion.

We construct the first examples of residually finite non-exact groups. The construction is based on author's earlier construction of groups containing isometrically expanders using a graphical small cancellation.

We initiate the study of torsion-free algebraically hyperbolic groups; these groups generalise torsion-free hyperbolic groups and are intricately related to groups with no Baumslag--Solitar subgroups. Indeed, for groups of cohomological…

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable;…

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

We study the subgroup structure of discrete groups which share cohomological properties which resemble non-negative curvature. Examples include all Gromov hyperbolic groups. We provide strong restrictions on the possible s-normal subgroups…

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely…

We show that there exist non-unitarizable groups without non-abelian free subgroups. Both torsion and torsion free examples are constructed. As a by-product, we show that there exist finitely generated torsion groups with non-vanishing…

We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented…

We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This gives new examples of groups acting uniformly properly on…

We construct a finitely generated residually finite group $G$ with the property that every finite index subgroup of $G$ contains a subgroup isomorphic to Promislow's group. Hence $G$ does not have a finite index subgroup with the unique…