• Corpus ID: 208164626

SUBGROUP DYNAMICS AND C∗-SIMPLICITY OF GROUPS OF HOMEOMORPHISMS

@inproceedings{Boudec2016SUBGROUPDA,
  title={SUBGROUP DYNAMICS AND C∗-SIMPLICITY OF GROUPS OF HOMEOMORPHISMS},
  author={Adrien Le Boudec},
  year={2016}
}
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… 
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References

SHOWING 1-10 OF 37 REFERENCES
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
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
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
A nonamenable finitely presented group of piecewise projective homeomorphisms
In this article we will describe a nitely presented subgroup of the group of piecewise projective homeomorphisms of the real projective line. is in particular provides a new example of a nitely
CUNTZ-PIMSNER ALGEBRAS OF GROUP ACTIONS
Abstract. We associate a ∗ -bimodule over the group algebra to every self-similar group action on the space of one-sided sequences. Completions ofthe group algebra, which agree with the bimodule are
...
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