• Corpus ID: 208164626


  author={Adrien Le Boudec},
We study the uniformly recurrent subgroups of groups acting by homeomorphisms on a topological space. We prove a general result relating uniformly recurrent subgroups to rigid stabilizers of the action, and deduce a C∗-simplicity criterion based on the non-amenability of rigid stabilizers. As an application, we show that Thompson’s group V is C∗-simple, as well as groups of piecewise projective homeomorphisms of the real line. This provides examples of finitely presented C∗-simple groups… 

Groups of piecewise linear homeomorphisms of flows

To every dynamical system $(X,\varphi )$ over a totally disconnected compact space, we associate a left-orderable group $T(\varphi )$. It is defined as a group of homeomorphisms of the suspension of

The ideal intersection property for essential groupoid C*-algebras

We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C∗-algebra has the ideal intersection property, assuming that

Rigidity properties of full groups of pseudogroups over the Cantor set

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies

On rigid stabilizers and invariant random subgroups of groups of homeomorphisms

A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an application, we

Piecewise strongly proximal actions, free boundaries and the Neretin groups

A closed subgroup H of a locally compact group G is confined if the closure of the conjugacy class of H in the Chabauty space of G does not contain the trivial subgroup. We establish a dynamical

Dynamical alternating groups, stability, property Gamma, and inner amenability

We prove that the alternating group of a topologically free action of a countably infinite group $\Gamma$ on the Cantor set has the property that all of its $\ell^2$-Betti numbers vanish and, in the

A commutator lemma for confined subgroups and applications to groups acting on rooted trees

A subgroup $H$ of a group $G$ is confined if the $G$-orbit of $H$ under conjugation is bounded away from the trivial subgroup in the space $\operatorname{Sub}(G)$ of subgroups of $G$. We prove a

Realizing uniformly recurrent subgroups

We show that every uniformly recurrent subgroup of a locally compact group is the family of stabilizers of a minimal action on a compact space. More generally, every closed invariant subset of the

C * -simplicity of HNN extensions and groups acting on trees

We study groups admitting extreme boundary actions, and in particular, groups acting on trees, and we give necessary and sufficient criteria for such groups to be C*-simple or have the unique trace

Groups of Automorphisms and Almost Automorphisms of Trees: Subgroups and Dynamics

These are notes of a lecture series delivered during the program Winter of Disconnectedness in Newcastle, Australia, 2016. The exposition is on several families of groups acting on trees by



Topological dynamics and group theory

We prove, using notions and techniques of topological dynamics, that a nonamenable group contains a finitely-generated subgroup of exponential growth. We also show that a group which belongs to a

Extensions of amenable groups by recurrent groupoids

We show that the amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class

Uniformly recurrent subgroups

We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in a work of M. Abert, Y. Glasner and B.

On minimal, strongly proximal actions of locally compact groups

Minimal, strongly proximal actions of locally compact groups on compact spaces, also known asboundary actions, were introduced by Furstenberg in the study of Lie groups. In particular, the action of

Subshifts with slow complexity and simple groups with the Liouville property

We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod

Invariant random subgroups of linear groups

AbstractLet Γ < GLn(F) be a countable non-amenable linear group with a simple, center free Zariski closure. Let Sub(Γ) denote the space of all subgroups of Γ with the compact, metric, Chabauty

C*-simplicity and the unique trace property for discrete groups

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical

Ideal structure of the C -algebra of Thompson group T

In a recent paper Ue Haagerup and Kristian Knudsen Olesen show that for Richard Thompson’s group T, if there exists a finite set H which can be decomposed as disjoint union of sets H1 and H2 with P

Boundaries of reduced C*-algebras of discrete groups

For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up