Graduation Year


Document Type




Degree Name

Master of Arts (M.A.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Dymtro Savchuk, Ph.D.

Committee Member

Mile Krajcevski, Ph.D.

Committee Member

Mohamed Elhamdadi, Ph.D.


amenable, gromov, cayley, action, homeomorphism


Thompson’s groups F, T, and V represent crucial examples of groups in geometric group theory that bridge it with other areas of mathematics such as logic, computer science, analysis, and geometry. One of the ways to study these groups is by understanding the geometric meaning of their actions. In this thesis we deal with Thompson’s group T that acts naturally on the unit circle S1, that is identified with the segment [0, 1] with the end points glued together. The main result of this work is the explicit construction of the Schreier graph of T with respect to the action on the orbit of 1/2. This is done by careful examination of patterns in how the generators of T act on binary words. As a main application, the nonamenability of the action of T on S1 is proved by defining injections on the set of vertices of the constructed graph that satisfy Gromov’s doubling condition. This gives an alternative proof of the known fact that T is nonamenable.

Included in

Mathematics Commons