We study the geometry of non-relatively hyperbolic groups. Generalizing a result of
Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively …

We give a complete characterization of the locally compact groups that are non elementary
Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete …

RANDOM WALKS ON THE MAPPING CLASS GROUP Page 1 RANDOM WALKS ON THE
MAPPING CLASS GROUP JOSEPH MAHER Abstract We show that a random walk on the …

We build an analogue of the Gromov boundary for any proper geodesic metric space, hence
for any finitely generated group. More precisely, for any proper geodesic metric space $ X …

A general fixed point theorem for isometries in terms of metric functionals is proved under
the assumption of the existence of a conical bicombing. It is new for isometries of convex …

We prove that when a countable group admits a nontrivial Floyd-type boundary, then every
nonelementary and metrically proper subgroup contains a noncommutative free subgroup …

Equivariant Embeddings of Trees into Hyperbolic Spaces Page 1 IMRN International
Mathematics Research Notices 2005, No. 22 Equivariant Embeddings of Trees into Hyperbolic …

We provide an analysis of the dynamics of isometries and semicontractions of metric spaces.
Certain subsets of the boundary at infinity play a fundamental role and are identified …

We establish growth tightness for a class of groups acting geometrically on a geodesic
metric space and containing a contracting element. As a consequence, any group with non …

We provide two new routes for studying the geometry of mapping class groups, and of
colourable hierarchically hyperbolic groups more generally. Firstly, we show that they are …