Richard Thompson group F is not amenable

2014/08/10 by Wajnryb, Bronislaw, Witowicz, Pawel
#20F38 #20F65 #20F67 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1408.2188

Abstract

Richard Thompson's group F is the group of piecewise linear homeomorphisms of the unit interval with a finite number of break points, all at dyadic rational numbers (their denominators are powers of 2) and with slopes which are powers of 2. A discrete group G is amenable if there exists a finitely-additive probability measure on G which is invariant under left translations and is defined on all subsets of G. The amenability question for F is a well known open problem. In this paper we prove that group F is not amenable.

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