## 130 Citations

### Growth of relatively hyperbolic groups

- Mathematics
- 2005

We show that a finitely generated group that is hyperbolic relative to a collection of proper subgroups either is virtually cyclic or has uniform exponential growth.

### Quasi-isometry rigidity of groups

- Mathematics
- 2006

This paper overviews recent developments in the classification up to quasi-isometry of finitely generated groups, and more specifically of relatively hyperbolic groups.

### Residual finiteness, QCERF, and fillings of hyperbolic groups

- Mathematics
- 2008

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

### Geometric group theory and hyperbolic geometry: Recent contributions from Indian mathematicians

- MathematicsIndian Journal of Pure and Applied Mathematics
- 2019

Geometric group theory emerged as a distinct branch of mathematics through the seminal work of Gromov [25] in 1987 and since then it has been a very active area of research intermingling with many…

### A note on hyperbolically embedded subgroups

- MathematicsCommunications in Algebra
- 2021

Abstract Let G be a group and H a subgroup of G. The notion of H being hyperbolically embedded in G was introduced by Dahmani, Guiraldel, and Osin. This note introduces an equivalent definition of…

### COMPLEX OF RELATIVELY HYPERBOLIC GROUPS

- MathematicsGlasgow Mathematical Journal
- 2018

Abstract In this paper, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin’s (Geom. Topology 18 (2014), 31–102) work for combination of…

### Height in splittings of relatively hyperbolic groups

- Mathematics
- 2015

Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups embed quasi-isometrically in vertex groups. We prove that a vertex group is…

### An obstruction to the strong relative hyperbolicity of a group

- Mathematics
- 2007

Abstract We give a simple combinatorial criterion for a group that, when satisfied, implies that the group cannot be strongly relatively hyperbolic. The criterion applies to several classes of…

## References

SHOWING 1-10 OF 12 REFERENCES

### Geometry of the complex of curves II: Hierarchical structure

- Physics
- 1998

Abstract. ((Without Abstract)).

### Subgroups of Word Hyperbolic Groups in Dimension 2

- Mathematics
- 1996

If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 and it is…

### Geometry of horospheres

- Mathematics
- 1977

Let M be a Hadamard manifold, i.e., a connected, simply connected, complete riemannian manifold of nonpositive curvature. To be more precise, assume that the sectional curvature K of M satisfies —…

### A note on curvature and fundamental group

- Mathematics
- 1968

Define the growth function γ associated with a finitely generated group and a specified choice of generators {gl7 -, gp} for the group as follows (compare [9]). For each positive integer s let γ(s)…

### Relatively hyperbolic and automatic groups with applications to negatively curved manifolds

- Mathematics
- 1994

### Manifolds of Nonpositive Curvature

- Mathematics
- 1985

Preface.-Introduction.-Lectures on Manifolds of Nonpositive Curvature.-Simply Connected Manifolds of Nonpositive Curvature.-Groups of Isometries.-Finiteness theorems.-Strong Rigidity of Locally…