Geometry and Topology
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California Polytechnic State University, San Luis Obispo
2022
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Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Jun 2022
Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Master's Theses
Given a presentation 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.
