On grid diagrams, braids and Markov moves

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dc.contributor.advisorGay, David Ten_ZA
dc.contributor.authorAyivor, Audry Fen_ZA
dc.date.accessioned2015-01-14T07:18:09Z
dc.date.available2015-01-14T07:18:09Z
dc.date.issued2010en_ZA
dc.descriptionIncludes abstract.en_ZA
dc.descriptionIncludes bibliographical references (leaves 42).en_ZA
dc.description.abstractGrid 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.en_ZA
dc.identifier.apacitationAyivor, A. F. (2010). <i>On grid diagrams, braids and Markov moves</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/12164en_ZA
dc.identifier.chicagocitationAyivor, Audry F. <i>"On grid diagrams, braids and Markov moves."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2010. http://hdl.handle.net/11427/12164en_ZA
dc.identifier.citationAyivor, A. 2010. On grid diagrams, braids and Markov moves. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ayivor, Audry F AB - 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. DA - 2010 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2010 T1 - On grid diagrams, braids and Markov moves TI - On grid diagrams, braids and Markov moves UR - http://hdl.handle.net/11427/12164 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/12164
dc.identifier.vancouvercitationAyivor AF. On grid diagrams, braids and Markov moves. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2010 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/12164en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleOn grid diagrams, braids and Markov movesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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