Geometric properties of the golden ratio Thompson’s group

Svetelik, Denys (2025) Geometric properties of the golden ratio Thompson’s group. MSc(R) thesis, University of Glasgow.

Abstract

We show that all three golden ratio Thompson’s groups Fτ , Tτ and Vτ embed in the asynchronous rational group. We prove properties of the Cayley graph of the monoid M = ⟨L, R : LR2 = RL2 ⟩, whose topological full group is Vτ . Particularly we compute a distance function for the Cayley graph of the monoid M. Additionally, we prove that this Cayley graph is hyperbolic in the sense of Gromov. Our analysis reveals that the horofunction boundary of this graph is homeomorphic to a space resembling a Cantor-like set, with additional isolated points situated between each pair of breakpoints.

• Item Type: Thesis (MSc(R))
• Qualification Level: Masters
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Whittaker, Professor Mike and Belk, Dr. Jim
• Date of Award: 2025
• Depositing User: Theses Team
• Unique ID: glathesis:2025-84844
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 29 Jan 2025 13:28
• Last Modified: 29 Jan 2025 13:30
• URI: https://theses.gla.ac.uk/id/eprint/84844