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arXiv · 2111.13616

A dichotomy for topological full groups

Eduardo Scarparo
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Abstract

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.

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Eduardo Scarparo. 2021-11-26. A dichotomy for topological full groups. https://arxiv.org/abs/2111.13616

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