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Burnside's Problem, spanning trees and tilings

2014
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Geometry and Topology
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In this paper we study geometric versions of Burnside's Problem and the von Neumann Conjecture. This is done by considering the notion of a translation-like action. Translation-like actions were introduced by Kevin Whyte as a geometric analogue of subgroup containment. Whyte proved a geometric version of the von Neumann Conjecture by showing that a finitely generated group is non-amenable if and only if it admits a translation-like action by any (equivalently every) non-abelian free group. We

doi:10.2140/gt.2014.18.179
fatcat:nkdspc2xfbgbrcadtmbvxcg47q