{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/4077"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/4077","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots","abstract":"After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P(-n,-m,m), where n and m are odd. This result shows that the rank of the Khovanov cohomology of P(-n-m,m) is an invariant of n.","abstract_html":"After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P(-n,-m,m), where n and m are odd. This result shows that the rank of the Khovanov cohomology of P(-n-m,m) is an invariant of n.","abstract_has_math":false,"creators":["Meier, Jeffrey"],"institution":null,"degree_name":null,"degree_level":"Master's Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Jabuka, Stanislav"],"committee_chairs":[],"committee_members":["Naik, Swatee","Hoelzer, Guy"],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-27T21:47:03Z","subjects":["Jones polynomial","Khovanov cohomology","Pretzel knots"],"languages":[],"rights":["In Copyright(All Rights Reserved)"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11714/4077","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jabuka, Stanislav"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Naik, Swatee","Hoelzer, Guy"]},{"key":"dc:creator","label":"Author","values":["Meier, Jeffrey"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-09-06T17:20:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-09-06T17:20:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's Degree"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Jones polynomial","Khovanov cohomology","Pretzel knots"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright(All Rights Reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11714/4077"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P(-n,-m,m), where n and m are odd. This result shows that the rank of the Khovanov cohomology of P(-n-m,m) is an invariant of n."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jabuka, Stanislav"],"dc:contributor.committeemember":["Naik, Swatee","Hoelzer, Guy"],"dc:creator":["Meier, Jeffrey"],"dc:date.accessioned":["2018-09-06T17:20:57Z"],"dc:date.available":["2018-09-06T17:20:57Z"],"dc:date.issued":["2009"],"dc:description.abstract":["After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P(-n,-m,m), where n and m are odd. This result shows that the rank of the Khovanov cohomology of P(-n-m,m) is an invariant of n."],"dc:format":["PDF"],"dc:identifier.uri":["http://hdl.handle.net/11714/4077"],"dc:rights":["In Copyright(All Rights Reserved)"],"dc:subject":["Jones polynomial","Khovanov cohomology","Pretzel knots"],"dc:title":["A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots"],"dc:type":["Thesis"],"thesis:degree_level":["Master's Degree"]},"updated_at":"2026-07-27T21:47:03Z"}