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Strongly Bounded Groups and Infinite Powers of Finite Groups
We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recentlyExpand
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuousExpand
Isometric Group Actions on Hilbert Spaces: Growth of Cocycles
Abstract.We study growth of 1-cocycles of locally compact groups, with values in unitary representations. Discussing the existence of 1-cocycles with linear growth, we obtain the followingExpand
We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under takingExpand
Normal subgroups in the Cremona group
Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane $$ \mathbb{P}_{\mathbf{k}}^2 $$ is not a simple group. The strategyExpand
Abstract We perform a systematic investigation of Kazhdan's relative Property (T) for pairs ( G , X ) , where G is a locally compact group and X is any subset. When G is a connected Lie group or aExpand
On the isolated points in the space of groups
We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groupsExpand
The Howe-Moore property for real and p-adic groups
We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodicExpand
Commensurating actions for groups of piecewise continuous transformations
We use partial actions, as formalized by Exel, to construct various commensurating actions. We use this in the context of groups piecewise preserving a geometric structure, and we interpret theExpand
Irreducible lattices, invariant means, and commensurating actions
We study rigidity properties of lattices in terms of invariant means and commensurating actions (or actions on CAT(0) cube complexes). We notably study Property FM for groups, namely that any actionExpand