26 citations · 123 across the 21 of their papers we have counts for
21 papers
The variety of group actions on all algebraic real hyperbolic spaces
Bruno Duchesne, Christopher-Lloyd Simon
For a cardinal , denote by the algebraic real hyperbolic space of dimension . For a topological group , we study the set of continuous representations $Γ\to…
Hyperbolic Simplices of Maximal Inradius
Bruno Duchesne, Christopher-Lloyd Simon
For , consider a hyperbolic -dimensional simplex , defined by points in the compactified hyperbolic space .…
Homeomorphism groups of basilica, rabbit and airplane Julia sets
Bruno Duchesne, Matteo Tarocchi
The airplane, the basilica and the Douady rabbit (and, more generally, rabbits with more than two ears) are well-known Julia sets of complex quadratic polynomials. In this paper we…
A group with Property (T) acting on the circle
Bruno Duchesne
We exhibit a topological group with property (T) acting non-elementarily and continuously on the circle. This group is an uncountable totally disconnected closed subgroup of $\…
The Polish topology of the isometry group of the infinite dimensional hyperbolic space
Bruno Duchesne
We consider the isometry group of the infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by the pointwise convergence. For non-locally…
Representations of infinite dimension orthogonal groups of quadratic forms with finite index
Bruno Duchesne
We study representations where is either a simple Lie group with real rank at least 2 or an infinite dimensional orthogonal group of some quadratic form of finite inde…
CAT(0) cube complexes and inner amenability
Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek
We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group on a finite dimensional irreduci…
Topological properties of Wazewski dendrite groups
Bruno Duchesne
Homeomorphism groups of generalized Ważewski dendrites act on the infinite countable set of branch points of the dendrite and thus have a nice Polish topology. In this paper, we st…
A new lattice invariant for lattices in totally disconnected locally compact groups
Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek
We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices…
Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
Bruno Duchesne, Jean Lécureux, Maria Beatrice Pozzetti
We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal repres…
Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms
Bruno Duchesne, Nicolas Monod, Phillip Wesolek
Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relat…
Structural properties of dendrite groups
Bruno Duchesne, Nicolas Monod
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Mo…
Group actions on dendrites and curves
Bruno Duchesne, Nicolas Monod
We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same hold…
Groups acting on spaces of non-positive curvature
Bruno Duchesne
In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show…
Almost algebraic actions of algebraic groups and applications to algebraic representations
Uri Bader, Bruno Duchesne, Jean Lécureux
Let G be an algebraic group over a complete separable valued field k. We discuss the dynamics of the G-action on spaces of probability measures on algebraic G-varieties. We show th…
Amenable Invariant Random Subgroups
Uri Bader, Bruno Duchesne, Jean Lecureux
We show that an amenable Invariant Random Subgroup of a locally compact second countable group lives in the amenable radical. This answers a question raised in the introduction of…
Geometric density for invariant random subgroups of groups acting on CAT(0) spaces
Bruno Duchesne, Yair Glasner, Nir Lazarovich +1
We prove that an IRS of a group with a geometrically dense action on a CAT(0) space also acts geometrically densely; assuming the space is either of finite telescopic dimension or…
Furstenberg Maps For CAT(0) Targets Of Finite Telescopic Dimension
Uri Bader, Bruno Duchesne, Jean Lécureux
We consider actions of locally compact groups on certain CAT(0) spaces by isometries. The CAT(0) spaces we consider have finite dimension at large scale. In case is a $…
Superrigidity In Infinite Dimension And Finite Rank Via Harmonic Maps
Bruno Duchesne
We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and…
Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator
Bruno Duchesne
We associate to any Riemannian symmetric space (of finite or infinite dimension) a L-algebra, under the assumption that the curvature operator has a fixed sign. L-algebras…
Infinite dimensional non-positively curved symmetric spaces of finite rank
Bruno Duchesne
This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisel…