Richard Thompson group F is not amenable
Group Theory
2015-03-10 v3
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.
Cite
@article{arxiv.1408.2188,
title = {Richard Thompson group F is not amenable},
author = {Bronislaw Wajnryb and Pawel Witowicz},
journal= {arXiv preprint arXiv:1408.2188},
year = {2015}
}
Comments
This paper has been withdrawn by the authors because the proof has a mistake which we cannot correct