A dichotomy for topological full groups

2021/11/26 by Scarparo, Eduardo
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2111.13616

Abstract

Given a minimal action α of a countable group on the Cantor set, we show that the alternating full group A(α) is non-amenable if and only if the topological full group F(α) is C^*-simple. This implies, for instance, that the Elek-Monod example of non-amenable topological full group coming from a Cantor minimal ℤ²-system is C^*-simple.

Related

• Amenable purely infinite actions on the non-compact Cantor set
• Dynamical alternating groups, stability, property Gamma, and inner amenability
• Soficity, Amenability, and LEF-ness for topological full groups
• Full groups of minimal homeomorphisms
• Locally compact piecewise full groups of homeomorphisms