On the topological full group of a minimal Cantor Z^2-system
arXiv:1201.0257 · doi:10.1090/S0002-9939-2013-11654-0
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.
3 pages (some comments added)