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arXiv · 1201.0257

On the topological full group of a minimal Cantor Z^2-system

Gabor Elek·Nicolas Monod
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Abstract

Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor 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 Z^2-action for which the topological full group contains a non-abelian free group.

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Gabor Elek, Nicolas Monod. 2011-12-31. On the topological full group of a minimal Cantor Z^2-system. https://doi.org/10.1090/s0002-9939-2013-11654-0

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