Van Kampen Diagrams and Small Cancellation Theory

<p>Given a presentation <a> of G, the word problem asks whether there exists an algorithm to determine which words in the free group, F(A), represent the identity in G. In this thesis, we study small cancellation theory, developed by Lyndon, Schupp, and Greendlinger in the mid-1960s, which contributed to the resurgence of geometric group theory. We investigate the connection between Van Kampen diagrams and the small cancellation hypotheses. Groups that have a presentation satisfying the small cancellation hypotheses C'(1/6), or C'(1/4) and T(4) have a nice solution to the word problem known as Dehn’s Algorithm.</a></p>

Name thesis:degree_name

MS in Mathematics

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2022

Author dc:creator

• Lowrey, Kelsey N

Contributors dc:contributor

• Anton Kaul
• Mathematics
• College of Science and Mathematics

• Word Problem
• Van Kampen Diagrams
• Small Cancellation Theory
• Dehn's Algorithm
• Geometric Group Theory
• Algebra
• Geometry and Topology
• Other Mathematics

Identifier

10.15368/theses.2022.37

OAI identifier oai:identifier

oai:digitalcommons.calpoly.edu:theses-4045