{"id":{"repo_id":"sfasu","oai_identifier":"oai:scholarworks.sfasu.edu:etds-1542"},"canonical_url":"https://search.dev.ndltd.org/etd/sfasu/oai:scholarworks.sfasu.edu:etds-1542","repository":{"repo_id":"sfasu","name":"Stephen F. Austin State University","base_url":"https://scholarworks.sfasu.edu/do/oai/"},"display":{"title":"Restrictions on Topological Symmetry Groups of the 3-Rung Möbius Ladder on the Torus","abstract":"<p>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 Z<sub>2</sub> is the only possible non-trivial orientation-preserving topological symmetry groups, and also that Z<sub>2</sub> and D<sub>2</sub> are the only possible nontrivial topological symmetry groups.</p>","abstract_html":"&lt;p&gt;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 Z&lt;sub&gt;2&lt;/sub&gt; is the only possible non-trivial orientation-preserving topological symmetry groups, and also that Z&lt;sub&gt;2&lt;/sub&gt; and D&lt;sub&gt;2&lt;/sub&gt; are the only possible nontrivial topological symmetry groups.&lt;/p&gt;","abstract_has_math":false,"creators":["Willhoite, Logan"],"institution":null,"degree_name":"Master of Science - Mathematical Sciences","degree_level":"Thesis","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":["Jane Long, Ph.D.","Clint Richardson, Ph.D.","Brittney Falahola, Ph.D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-05-06T07:00:00Z","date_published":"2023-05-06T07:00:00Z","updated_at":"2026-07-24T04:30:45Z","subjects":["topology","möbius ladder","symmetry groups","torus","embeddings","stereochemistry","Algebra","Geometry and Topology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/512","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jane Long, Ph.D.","Clint Richardson, Ph.D.","Brittney Falahola, Ph.D."]},{"key":"dc:creator","label":"Author","values":["Willhoite, Logan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2024-05-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Mathematical Sciences"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["topology","möbius ladder","symmetry groups","torus","embeddings","stereochemistry","Algebra","Geometry and Topology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/512"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>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 Z<sub>2</sub> is the only possible non-trivial orientation-preserving topological symmetry groups, and also that Z<sub>2</sub> and D<sub>2</sub> are the only possible nontrivial topological symmetry groups.</p>"]},{"key":"dc:title","label":"Title","values":["Restrictions on Topological Symmetry Groups of the 3-Rung Möbius Ladder on the Torus"]}]}],"canonical_facts":{"dc:contributor":["Jane Long, Ph.D.","Clint Richardson, Ph.D.","Brittney Falahola, Ph.D."],"dc:creator":["Willhoite, Logan"],"dc:date.available":["2024-05-07T07:00:00Z"],"dc:description.abstract":["<p>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 Z<sub>2</sub> is the only possible non-trivial orientation-preserving topological symmetry groups, and also that Z<sub>2</sub> and D<sub>2</sub> are the only possible nontrivial topological symmetry groups.</p>"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/512"],"dc:subject":["topology","möbius ladder","symmetry groups","torus","embeddings","stereochemistry","Algebra","Geometry and Topology"],"dc:title":["Restrictions on Topological Symmetry Groups of the 3-Rung Möbius Ladder on the Torus"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Mathematical Sciences"]},"updated_at":"2026-07-24T04:30:45Z"}