JournalsggdVol. 14, No. 1pp. 61–79

On topological full groups of Zd\mathbb 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 Zd\mathbb Z^d-actions. Groups Geom. Dyn. 14 (2020), no. 1, pp. 61–79

DOI 10.4171/GGD/534