On rigid stabilizers and invariant random subgroups of groups of homeomorphisms

Abstract

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 classify ergodic invariant random subgroups of topological full groups of Cantor minimal ${\mathbb{Z}}^d$-systems. Another corollary is that for an ergodic invariant random subgroup of a branch group, a.e. subgroup $H$ must contain derived subgroups of certain rigid stabilizers. Such results can be applied towards classification of invariant random subgroups of Grigorchuk groups.

References in corpus (2)

• Rigidity properties of full groups of pseudogroups over the Cantor set
• On Invariant Random Subgroups of Block-Diagonal Limits of Symmetric Groups

Cited by in corpus (2)

• Infinitely presented stable groups and invariant random subgroups of metabelian groups
• Neretin groups admit no non-trivial invariant random subgroups