Restrictions on Topological Symmetry Groups of the 3-Rung Möbius Ladder on the Torus

Author

Logan Willhoite, Stephen F Austin State UniversityFollow

Date of Award

Spring 5-6-2023

Degree Type

Thesis

Degree Name

Master of Science - Mathematical Sciences

Department

Mathematics and Statistics

First Advisor

Jane Long, Ph.D.

Second Advisor

Clint Richardson, Ph.D.

Third Advisor

Brittney Falahola, Ph.D.

Fourth Advisor

Alyx Frantzen, Ph.D.

Abstract

In this work, we discuss properties of the 3-rung Möbius ladder embedded on the surface of a torus. We present proofs on restrictions of topological symmetry groups of the Möbius ladder with and without the assumption of preserving orientation. Specifically, we show that Z₂ is the only possible non-trivial orientation-preserving topological symmetry groups, and also that Z₂ and D₂ are the only possible nontrivial topological symmetry groups.

Repository Citation

Willhoite, Logan, "Restrictions on Topological Symmetry Groups of the 3-Rung Möbius Ladder on the Torus" (2023). Electronic Theses and Dissertations. 512.
https://scholarworks.sfasu.edu/etds/512

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.