Geodesic
A dichotomy for topological full groups
Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 610-616

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DOI

Given a minimal action $\alpha $ of a countable group on the Cantor set, we show that the alternating full group $\mathsf {A}(\alpha )$ is non-amenable if and only if the topological full group $\mathsf {F}(\alpha )$ is $C^*$-simple. This implies, for instance, that the Elek–Monod example of non-amenable topological full group coming from a Cantor minimal $\mathbb {Z}^2$-system is $C^*$-simple.
DOI : 10.4153/S000843952200056X
Mots-clés : Topological full groups, C*-simplicity, amenability 
Scarparo, Eduardo. A dichotomy for topological full groups. Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 610-616. doi: 10.4153/S000843952200056X
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