Date of Graduation
5-2024
Document Type
Thesis
Degree Name
Bachelor of Science in Mathematics
Degree Level
Undergraduate
Department
Mathematical Sciences
Advisor/Mentor
Day, Matthew
Committee Member/Reader
Hare, Laurence
Committee Member/Second Reader
Vyas, Reeta
Committee Member/Third Reader
Miller, Lance
Abstract
Surfaces have long been a topic of interest for scholars inside and outside of mathe- matics. In a topological sense, surfaces are spaces which appear flat on a local scale. Surfaces in this sense have a restricted set of properties, including the behavior of loops around a surface, codified in the fundamental group.
All but 3 surface groups have been shown to embed into a class of groups called right-angled Artin groups. The method through which these embeddings are created places large restrictions on all homomorphisms from surface groups to right-angled Artin groups.
One such restriction on these homomorphisms is on distortion. A group can be represented by a graph, where distortion codifies how shortcuts can be found outside of a subgraph. It has already been shown that, for all relevant surface groups, there exists at least one undistorted embedding inside of a right-angled Artin group. Theorem A and Conjecture B seek to extend this to all homomorphisms.
Keywords
Distortion; Surfaces; Surface Groups; Graph Groups; Right-Angled Artin Groups
Citation
Bridges, L. (2024). On Distortion of Surface Groups in Right-Angled Artin Groups. Mathematical Sciences Undergraduate Honors Theses Retrieved from https://scholarworks.uark.edu/mascuht/7
