Related papers: On definitions of relatively hyperbolic groups

This article is dedicated to the characterisation of the relative hyperbolicity of Haglund and Wise's special groups. More precise, we introduce a new combinatorial formalism to study (virtually) special groups, and we prove that, given a…

We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…

In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.

Let Gamma be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin-Razborov diagrams for Gamma. We also prove that every system of equations over Gamma is equivalent to a finite…

We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. Using the fine graph approach to relative hyperbolicity, we find short proofs of the relative hyperbolicity of G under certain…

We consider two families of subgroups of a group. Each subgroup which belongs to one family is contained in some subgroup which belongs to the other family. We then discuss relations of relative hyperbolicity for the group with respect to…

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.

We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability,…

In this article, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin's \cite{martin} work for combination of hyperbolic groups over a finite $M_K$-simplicial complex, where $k\leq…

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…

In this paper, we prove a combination theorem for a relatively acylindrical graph of relatively hyperbolic groups (Theorem 1.1). Here, we are extending the technique of [Tom21] and constructing Bowditch boundary of the fundamental group of…

F. Paulin proved that if the Gromov boundaries of two hyperbolic groups are quasi-Mobius equivalent, then the groups themselves are quasi-isometric. The goal of this article is to extend Paulin's result to the setting of relatively…

Let f be a dominant rational map of P^k such that there exists s <k, with lambda_s(f)>lambda_l(f) for all l. Under mild hypotheses, we show that, for A outside a pluripolar set of the group of automorphisms of P^k, the map f o A admits a…

This paper shows that every Gromov hyperbolic group can be described by a finite subdivision rule acting on the 3-sphere. This gives a boundary-like sequence of increasingly refined finite cell complexes which carry all quasi-isometry…

Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups…

Let G be a finitely generated relatively hyperbolic group. We show that if no peripheral subgroup of G is hyperbolic relative to a collection of proper subgroups, then the fixed subgroup of every automorphism of G is relatively quasiconvex.…

We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.

The aim of these notes is to connect the theory of hyperbolic and relatively hyperbolic groups to the theory of manifolds and Kleinian groups. We survey some of the extensive work that has been done in the field, and explain many examples.…

We prove the following boundary-theoretic characterization of relatively hyperbolic groups. Let $G$ be a finitely generated group with a finite collection $\mathcal{H}$ of finitely generated subgroups, and let $G^h$ denote the associated…

Gromov Hyperbolic groups have remarkable finiteness properties;for example those that are torsion-free are fundamental groups of finitecomplexes whose universal cover iscontractible (property~$F$). In this talk we will show thattheir…