On the stabilisers of points in groups with micro-supported actions-Reference-Cited by-同舟云学术

On the stabilisers of points in groups with micro-supported actions

Published:2020-12-22 Issue:3 Volume:24 Page:533-547
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Francoeur Dominik¹

Affiliation:

1. UMPA , ENS de Lyon , Lyon , France

Abstract

Abstract Given a group 𝐺 of homeomorphisms of a first-countable Hausdorff space 𝒳, we prove that if the action of 𝐺 on 𝒳 is minimal and has rigid stabilisers that act locally minimally, then the neighbourhood stabilisers of any two points in 𝒳 are conjugated by a homeomorphism of 𝒳. This allows us to study stabilisers of points in many classes of groups, such as topological full groups of Cantor minimal systems, Thompson groups, branch groups, and groups acting on trees with almost prescribed local actions.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2020-0145/pdf

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