EVENT DETAILS AND ABSTRACT

Title: On simple amenable groups
Speaker: Kate Juschenko
Speaker Info: Vanderbilt University
Brief Description:
Special Note:
Abstract:

I will discuss amenability of the topological full group of a minimal Cantor system. Together with the results of H. Matui this provides examples of finitely generated simple amenable groups. For a metric space (X,d) define a group W(X) as a group of all bijections g of X such that sup{ d(g(x),x) : x in X } is finite. An important ingredient of the proof of amenability of the full topological group is a construction of an W(Z)-invariant mean on the set of finite subsets of integers. In fact, one can show more for a general metric spaces: if X satisfies Sobolev inequality then there is W(X)-invariant mean on finite subsets of X.