Colloquium

Thursday, March 27, 2008

4:00 PM, BAC 219

Speaker: Dan Farley, Miami University, Oxford, Ohio

Visiting Assistant Professor

Title: A Weak Form of Amenability for Thompson's Groups

Abstract:  Thompson's group F is a group piecewise-linear homeomorphisms of the unit interval [0,1].  It is a long-standing open question to determine whether F is amenable, and this question motivates much of the research about Thompson's group today. It has been conjectured by Geoghegan that F is a finitely presented, non-amenable group with no free subgroups.  (The first example of a group with these properties was found by Sapir and Olshanskii in recent years, and solved an old problem posed by von Neumann.)

I will show that F satisfies a weak form of amenability, known as a-T-menability.  I will also discuss joint work in progress with Bruce Hughes, in which we describe a general class of groups, including F, that are also a-T-menable.  This class includes Brin's group nV, among others.