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A Tits alternative for topological full groups

Published online by Cambridge University Press:  27 August 2019

NÓRA GABRIELLA SZŐKE*
Affiliation:
Institut Fourier, Université Grenoble Alpes, France email [email protected]

Abstract

We prove a Tits alternative for topological full groups of minimal actions of finitely generated groups. On the one hand, we show that topological full groups of minimal actions of virtually cyclic groups are amenable. By doing so, we generalize the result of Juschenko and Monod for $\mathbf{Z}$-actions. On the other hand, when a finitely generated group $G$ is not virtually cyclic, then we construct a minimal free action of $G$ on a Cantor space such that the topological full group contains a non-abelian free group.

Type
Original Article
Copyright
© Cambridge University Press, 2019

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