There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots.
","abstract_html":"<p>There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots.</p>","abstract_has_math":false,"creators":["Haskell, Jason"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Math and Computer Science","degree_department":null,"school":null,"contributors":["Joshua Thompson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-04-01T07:00:00Z","date_published":"2022-04-01T07:00:00Z","updated_at":"2026-07-24T03:24:24Z","subjects":["quandle","knot","subquandle","involutory","fundamental","Reidemeister","tricolorability","invariant","oriented","Algebra","Geometry and Topology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.nmu.edu/theses/698","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Joshua Thompson"]},{"key":"dc:creator","label":"Author","values":["Haskell, Jason"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-04-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Math and Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quandle","knot","subquandle","involutory","fundamental","Reidemeister","tricolorability","invariant","oriented","Algebra","Geometry and Topology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.nmu.edu/theses/698"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots.
"]},{"key":"dc:title","label":"Title","values":["Quandles that are Knot Quandles"]}]}],"canonical_facts":{"dc:contributor":["Joshua Thompson"],"dc:creator":["Haskell, Jason"],"dc:date.available":["2022-04-01T07:00:00Z"],"dc:description.abstract":["There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots.
"],"dc:identifier":["https://commons.nmu.edu/theses/698"],"dc:subject":["quandle","knot","subquandle","involutory","fundamental","Reidemeister","tricolorability","invariant","oriented","Algebra","Geometry and Topology"],"dc:title":["Quandles that are Knot Quandles"],"thesis:degree_discipline":["Math and Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T03:24:24Z"}