In this paper we develop some of the foundations of the theory of relatively hyperbolic
groups as originally formulated by Gromov. We prove the equivalence of two definitions of …

The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

arXiv:math/0202286v1 [math.GR] 27 Feb 2002 Page 1 arXiv:math/0202286v1 [math.GR] 27 Feb
2002 2000]Primary: 20F67; Secondary: 19K, 20F65, 20F69, 22E, 22D, 30C, 30F, 43A, 46E, 46L …

In this paper, we give a construction of the JSJ splitting of a one-ended hyperbolic group (in
the sense of Gromov [Gr]), using the local cut point structure of the boundary. In particular …

This is a survey of decision problems for groups, that is of algorithms for answering various
questions about groups and their elements. The general objective of this area can be …

Conformal dimension measures the extent to which the Hausdorff dimension of a metric
space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this …

Résumé Les objets que nous étudions sont les espaces métriques munis d'une action par
isométrie d'un groupe fixé Γ. Nous définissons une «topologie» naturelle sur «l'ensemble» …

The classification of stable actions of finitely presented groups on ℝ-trees has found a
number of applications. Perhaps one of the most striking of these applications is the theory …

We study the B (6) and B (4)-T (4) small cancellation groups. These classes include the
usual C'(1/6) and C'(1/4)-T (4) metric small cancellation groups. We show that every finitely …

We define the notion of acylindrical graph of groups of a group. We bound the combinatorics
of these graphs of groups for fg freely indecomposable groups. Our arguments imply the …