Nonassociative Ramsey Theory and the amenability of Thompson's group
arXiv:1209.2063
Abstract
The purpose of this article is prove that Thompson's group F is amenable. The methods developed will then be used to prove a generalization of Hindman's theorem for the free nonassociative binary system on one generator.
Over the weekend of September 29-30, 2012, Azer Akhmedov pointed out a serious error in Lemma 4.13. This error appears to be both serious and irreparable. I therefore withdraw my claim of a proof that F is amenable