Binghamton University


MATHEMATICAL SCIENCES
COLLOQUIUM


DATE: February 5, 2009
TIME: 4:30 - 5:30 PM
PLACE: LN 2205
SPEAKER: Dmytro Savchuk, Texas A&M University
TITLE: Graphs related to Thompson's group F

Abstract


Perhaps, the most intriguing open question about Thompson's group F is whether or not it is amenable. We approach this question from two different points of view.

On the one hand we explicitly construct the Schreier graphs of Thompson's group F with respect to the stabilizers of each irrational or dyadic rational point of the interval [0,1] and the standard generating set {x_0, x_1}, and show that these graphs are amenable.

On the other hand we describe the structure of an induced subgraph of the Cayley graph of F with respect to the generating set {x_0,x_1}, containing all vertices of the form x_nw for w in the monoid generated by x_0 and x_1 and n>=0. We show that this graph is non-amenable.

Unfortunately, none of the above approaches gives the answer to the ultimate question about the amenability of F, but both shed some light on the structure of the group itself.


R E F R E S H M E N T S

4:00 to 4:25 PM
Kenneth W. Anderson
Memorial Reading Room