{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/12164"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/12164","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"On grid diagrams, braids and Markov moves","abstract":"Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy.","abstract_html":"Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy.","abstract_has_math":false,"creators":["Ayivor, Audry F"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Gay, David T"],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-22T22:22:44Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/12164","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gay, David T"]},{"key":"dc:creator","label":"Author","values":["Ayivor, Audry F"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-01-14T07:18:09Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-01-14T07:18:09Z"]},{"key":"dc:date.issued","label":"Date","values":["2010"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/12164"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes abstract.","Includes bibliographical references (leaves 42)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy."]},{"key":"dc:title","label":"Title","values":["On grid diagrams, braids and Markov moves"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gay, David T"],"dc:creator":["Ayivor, Audry F"],"dc:date.accessioned":["2015-01-14T07:18:09Z"],"dc:date.available":["2015-01-14T07:18:09Z"],"dc:date.issued":["2010"],"dc:description":["Includes abstract.","Includes bibliographical references (leaves 42)."],"dc:description.abstract":["Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy."],"dc:identifier.uri":["http://hdl.handle.net/11427/12164"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["On grid diagrams, braids and Markov moves"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:44Z"}