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arXiv · 1901.04428

On rigid stabilizers and invariant random subgroups of groups of homeomorphisms

Tianyi Zheng
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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.

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Tianyi Zheng. 2019-01-14. On rigid stabilizers and invariant random subgroups of groups of homeomorphisms. https://arxiv.org/abs/1901.04428

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