Topological full groups of etale groupoids

2016/02/01 by Matui, Hiroki · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1602.00383

Abstract

This is a survey of the recent development of the study of topological full groups of etale groupoids on the Cantor set. Etale groupoids arise from dynamical systems, e.g. actions of countable discrete groups, equivalence relations. Minimal Z-actions, minimal Z^N-actions and one-sided shifts of finite type are basic examples. We are interested in algebraic, geometric and analytic properties of topological full groups. More concretely, we discuss simplicity of commutator subgroups, abelianization, finite generation, cohomological finiteness properties, amenability, the Haagerup property, and so on. Homology groups of etale groupoids, groupoid C*-algebras and their K-groups are also investigated.

Cited by

• Ample groupoids that are neither almost finite nor purely infinite
• Embedding groups into acyclic groups

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• Etale groupoids arising from products of shifts of finite type
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