{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/558"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/558","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots","abstract":"Symmetric unions, originally introduced in 1957 by Shin'ichi Kinoshita and Hide- taka Terasaka [3], have since been studied due to their failure to be distinguished by some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new invariant, Khovanov Homology, which gives more information (an entire homology) than some more classic invariants. In this paper, we look at Khovanov Homology's ability to distinguish or classify symmetric unions of particular knots. We are able to show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus knots and certain other 2-bridge knots.","abstract_html":"Symmetric unions, originally introduced in 1957 by Shin'ichi Kinoshita and Hide- taka Terasaka [3], have since been studied due to their failure to be distinguished by some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new invariant, Khovanov Homology, which gives more information (an entire homology) than some more classic invariants. In this paper, we look at Khovanov Homology's ability to distinguish or classify symmetric unions of particular knots. We are able to show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus knots and certain other 2-bridge knots.","abstract_has_math":false,"creators":["Gafney, T. .J."],"institution":"University of Nevada, Reno","degree_name":"Mathematics","degree_level":"Honors Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Jabuka, Stanislav"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-27T21:48:09Z","subjects":[],"languages":["en_US","English"],"rights":["In Copyright(All Rights Reserved)"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11714/558","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:creator","label":"Author","values":["Gafney, T. .J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-01-24T23:09:10Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-01-24T23:09:10Z"]},{"key":"dc:date.issued","label":"Date","values":["2011"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Honors Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Nevada, Reno"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"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/11714/558"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The University of Nevada, Reno Libraries will promptly respond to removal requests related to content that violates intellectual property laws, data protections, or has been uploaded without creator consent. Takedown notices should be directed to our ScholarWolf team (scholarwolf@library.unr.edu) with information about the object, including its full URL and the nature of your complaint."]},{"key":"dc:description.abstract","label":"Abstract","values":["Symmetric unions, originally introduced in 1957 by Shin'ichi Kinoshita and Hide- taka Terasaka [3], have since been studied due to their failure to be distinguished by some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new invariant, Khovanov Homology, which gives more information (an entire homology) than some more classic invariants. In this paper, we look at Khovanov Homology's ability to distinguish or classify symmetric unions of particular knots. We are able to show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus knots and certain other 2-bridge knots."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jabuka, Stanislav"],"dc:creator":["Gafney, T. .J."],"dc:date.accessioned":["2017-01-24T23:09:10Z"],"dc:date.available":["2017-01-24T23:09:10Z"],"dc:date.issued":["2011"],"dc:description":["The University of Nevada, Reno Libraries will promptly respond to removal requests related to content that violates intellectual property laws, data protections, or has been uploaded without creator consent. Takedown notices should be directed to our ScholarWolf team (scholarwolf@library.unr.edu) with information about the object, including its full URL and the nature of your complaint."],"dc:description.abstract":["Symmetric unions, originally introduced in 1957 by Shin'ichi Kinoshita and Hide- taka Terasaka [3], have since been studied due to their failure to be distinguished by some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new invariant, Khovanov Homology, which gives more information (an entire homology) than some more classic invariants. In this paper, we look at Khovanov Homology's ability to distinguish or classify symmetric unions of particular knots. We are able to show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus knots and certain other 2-bridge knots."],"dc:format":["PDF"],"dc:identifier.uri":["http://hdl.handle.net/11714/558"],"dc:language":["English"],"dc:language.iso":["en_US"],"dc:rights":["In Copyright(All Rights Reserved)"],"dc:title":["Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots"],"dc:type":["Thesis"],"thesis:degree_level":["Honors Thesis"],"thesis:degree_name":["Mathematics"],"thesis:institution_name":["University of Nevada, Reno"]},"updated_at":"2026-07-27T21:48:09Z"}