Tony Guttmann - On the amenability of Thompson's Group F скачать в хорошем качестве

Tony Guttmann - On the amenability of Thompson's Group F

In 1967 Richard Thompson introduced the group F, hoping that it was non-amenable, since then it would disprove the von Neumann conjecture. Though the conjecture has subsequently been disproved, the question of the amenability of Thompson's group F has still not been rigorously settled. In this talk I will present the most comprehensive numerical attack on this problem that has yet been mounted. I will first give a history of the problem, including mention of the many incorrect "proofs" of amenability or non-amenability. Then I will give details of a new, efficient algorithm for obtaining terms of the co-growth sequence. Finally I will describe a number of numerical methods to analyse the co-growth sequences of a number of infinite, finitely-generated groups, and show how these methods provide compelling evidence (though of course not a proof) that Thompson's group F is not amenable. I will also describe an alternative route to a rigorous proof. (This is joint work with Andrew Elvey Price). The talk is based on a material presented in a preprint https://arxiv.org/abs/1706.07571 For more information on the Zero-dimensional symmetry research group at the University of Newcastle and the Symmetries in Newcastle seminar series please visit https://zerodimensional.group/