Graduation Year
2017
Document Type
Thesis
Degree
M.A.
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.
Keywords
amenable, gromov, cayley, action, homeomorphism
Abstract
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.
Scholar Commons Citation
Pennington, Allen, "Schreier Graphs of Thompson's Group T" (2017). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/6740
