On topological full groups of $\mathbb Z^d$-actions

Maksym Chornyi; Kate Juschenko; Volodymyr V. Nekrashevych

doi:10.4171/ggd/534

JournalsggdVol. 14, No. 1pp. 61–79

On topological full groups of $Z^{d}$ -actions

Maksym Chornyi
Northwestern University, Evanston, USA
Kate Juschenko
University of Texas at Austin, USA
Volodymyr V. Nekrashevych
Texas A&M University, College Station, USA

$On topological full groups of $\mathbb Z^d$-actions cover$

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Abstract

We give new examples of simple finitely generated groups arising from actions of free abelian groups on the Cantor sets. As particular examples, we discuss groups of interval exchange transformations, and a group naturally associatedwith the Penrose tilings. Many groups in this class are amenable.

Cite this article

Maksym Chornyi, Kate Juschenko, Volodymyr V. Nekrashevych, On topological full groups of $Z^{d}$ -actions. Groups Geom. Dyn. 14 (2020), no. 1, pp. 61–79

DOI 10.4171/GGD/534