On the topological full group of a minimal Cantor 𝐙²-system

Elek, Gábor; Monod, Nicolas

doi:10.1090/S0002-9939-2013-11654-0

On the topological full group of a minimal Cantor $\mathbf {Z}^2$-system
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by Gábor Elek and Nicolas Monod PDF

Proc. Amer. Math. Soc. 141 (2013), 3549-3552 Request permission

Abstract:

Grigorchuk and Medynets recently conjectured that the topological full group of a minimal Cantor $\mathbf {Z}$-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the negative by producing a minimal Cantor $\mathbf {Z}^2$-action for which the topological full group contains a non-abelian free group.

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