We introduce a number of new tools for the study of relatively hyperbolic groups. First, given
a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model …

We establish new results and introduce new methods in the theory of measurable orbit
equivalence, using bounded cohomology of group representations. Our rigidity statements …

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 …

In this paper and its companion [31], we introduce new techniques and results in an attempt
to extend rigidity theory beyond the scope of linear groups. Amongst our main tools is the …

R.–Ozawa a montré dans [21] que, pour un groupe cci hyperbolique, le facteur de type II1
associé est solide. En devéloppant une nouvelle approche, qui combine les méthodes de …

The title refers to the area of research which studies infinite groups using measure-theoretic
tools, and studies the restrictions that group structure imposes on ergodic theory of their …

A selection of aspects of the theory of bounded cohomology is presented. The emphasis is
on questions motivating the use of that theory as well as on some concrete issues suggested …

Kac–Moody groups over finite fields are finitely generated groups. Most of them can
naturally be viewed as irreducible lattices in products of two closed automorphism groups of …

Let G be a group, H a hyperbolically embedded subgroup of G, V a normed G–module, U an
H–invariant submodule of V. We propose a general construction which allows to extend 1 …

We define a bounded cohomology class, called the median class, in the second bounded
cohomology, with appropriate coefficients, of the automorphism group of a finite-dimensional …