{"id":{"repo_id":"calpoly","oai_identifier":"oai:digitalcommons.calpoly.edu:theses-4045"},"canonical_url":"https://search.dev.ndltd.org/etd/calpoly/oai:digitalcommons.calpoly.edu:theses-4045","repository":{"repo_id":"calpoly","name":"Cal Poly","base_url":"https://digitalcommons.calpoly.edu/do/oai/"},"display":{"title":"Van Kampen Diagrams and Small Cancellation Theory","abstract":"<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>","abstract_html":"&lt;p&gt;Given a presentation &lt;a&gt; 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&#x27;(1/6), or C&#x27;(1/4) and T(4) have a nice solution to the word problem known as Dehn’s Algorithm.&lt;/a&gt;&lt;/p&gt;","abstract_has_math":false,"creators":["Lowrey, Kelsey N"],"institution":null,"degree_name":"MS in Mathematics","degree_level":null,"degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Anton Kaul","Mathematics","College of Science and Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-06-01T07:00:00Z","date_published":"2022-06-01T07:00:00Z","updated_at":"2026-07-24T01:32:29Z","subjects":["Word Problem","Van Kampen Diagrams","Small Cancellation Theory","Dehn's Algorithm","Geometric Group Theory","Algebra","Geometry and Topology","Other Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2022.37"],"render_values":[{"text":"10.15368/theses.2022.37","href":"https://doi.org/10.15368/theses.2022.37","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/2647","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Anton Kaul","Mathematics","College of Science and Mathematics"]},{"key":"dc:creator","label":"Author","values":["Lowrey, Kelsey N"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-06-06T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Word Problem","Van Kampen Diagrams","Small Cancellation Theory","Dehn's Algorithm","Geometric Group Theory","Algebra","Geometry and Topology","Other Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/2647","10.15368/theses.2022.37"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<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>"]},{"key":"dc:title","label":"Title","values":["Van Kampen Diagrams and Small Cancellation Theory"]}]}],"canonical_facts":{"dc:contributor":["Anton Kaul","Mathematics","College of Science and Mathematics"],"dc:creator":["Lowrey, Kelsey N"],"dc:date.available":["2022-06-06T07:00:00Z"],"dc:description.abstract":["<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>"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/2647","10.15368/theses.2022.37"],"dc:subject":["Word Problem","Van Kampen Diagrams","Small Cancellation Theory","Dehn's Algorithm","Geometric Group Theory","Algebra","Geometry and Topology","Other Mathematics"],"dc:title":["Van Kampen Diagrams and Small Cancellation Theory"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_name":["MS in Mathematics"]},"updated_at":"2026-07-24T01:32:29Z"}