Logic Seminar

It is an old question whether Thompson's group F is amenable or not. To prove that F is not amenable, we can show that F is not Liouville for any generating measure on F. By looking at its action on the set of dyadic rationals, one can show that for finitely supported generating measures, F is not Liouville, which could be a first step in proving that F is not amenable. There is a subclass of amenable groups, called strongly amenable groups. These are the groups for which every proximal action on a compact Hausdorff space has a fixed point. We can modify the usual action of F on dyadic rationals to prove that F is not strongly amenable.