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On grid diagrams, braids and Markov moves
Includes abstract.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613183430098944 |
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| access_status_str | Open Access |
| author | Ayivor, Audry F |
| author2 | Gay, David T |
| author_browse | Ayivor, Audry F Gay, David T |
| author_facet | Gay, David T Ayivor, Audry F |
| author_sort | Ayivor, Audry F |
| collection | Thesis |
| description | Includes abstract. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/12164 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:06.010Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/12164 On grid diagrams, braids and Markov moves Ayivor, Audry F Gay, David T Mathematics and Applied Mathematics Includes abstract. Includes bibliographical references (leaves 42). 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. 2015-01-14T07:18:09Z 2015-01-14T07:18:09Z 2010 Master Thesis Masters MSc http://hdl.handle.net/11427/12164 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Ayivor, Audry F On grid diagrams, braids and Markov moves |
| thesis_degree_str | Master's |
| title | On grid diagrams, braids and Markov moves |
| title_full | On grid diagrams, braids and Markov moves |
| title_fullStr | On grid diagrams, braids and Markov moves |
| title_full_unstemmed | On grid diagrams, braids and Markov moves |
| title_short | On grid diagrams, braids and Markov moves |
| title_sort | on grid diagrams braids and markov moves |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/12164 |
| work_keys_str_mv | AT ayivoraudryf ongriddiagramsbraidsandmarkovmoves |