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Oriented 123-TQFTs via String-Nets and State-Sums
Thesis (PhD)--Stellenbosch University, 2018.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2018
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| _version_ | 1867613786897121280 |
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| access_status_str | Open Access |
| author | Goosen, Gerrit |
| author2 | Bartlett, Bruce |
| author_browse | Bartlett, Bruce Goosen, Gerrit |
| author_facet | Bartlett, Bruce Goosen, Gerrit |
| author_sort | Goosen, Gerrit |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2018. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/103324 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:41:41.074Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/103324 Oriented 123-TQFTs via String-Nets and State-Sums Goosen, Gerrit Bartlett, Bruce Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. String nets (Mathematics) UCTD Quantum field theories Turaev-Viro theory State space (Mathematics) Thesis (PhD)--Stellenbosch University, 2018. ENGLISH ABSTRACT :In a series of papers Bartlett, Douglas, Schommer-Pries, and Vicary discovered a finite generators-and-relations presentation of the oriented bordism bicategory. This simplifies the task of finding oriented once-extended topological quantum field theories (123-TQFTs). We combine this result with the theory of string-nets, specifically Kirillov’s generalization of the theory to surfaces with boundary, and construct an oriented 123-TQFT based on string-nets. Previously, string-nets were only understood at the level of surfaces - in particular, it was not known how to assign linear maps to cobordisms which changed the topology of the surface. We also reformulate the extended Turaev-Viro theory developed by Balsam and Kirillov into the bicategorical generators-and-relations formalism, and use this to prove that the string-net and Turaev-Viro 123-TQFTs are equivalent. AFRIKAANSE OPSOMMING : In ’n reeks artikels het Bartlett, Douglas, Schommer-Pries, en Vicary ’n eindige voortbringer-en-verwantskap voorstelling van die ge¨orienteerde kobordisme bikategorie ontdek. Hierdie voorstelling vergemaklik die taak om ge¨orienteerde eenmaaluitgebreide topologiese kwantumveldtoerie¨e (123- TKVTe) op te spoor. Ons kombineer hierdie resultaat met die teorie van string-nette, veral Kirillov se veralgemening van die teorie na begrensde oppervlakke, om sodoende ’n ge¨orienteerde 123-TKVT gebaseer op stringnette te konstrueer. Voorheen was die teorie slegs verstaan vir oppervlakke - byvoorbeeld, dit was nie bekend hoe om ’n lineˆere transformasie te assosieer met ’n kobordisme wat die topologie van die onderlinge ruimte verander nie. Ons herformuleer ook die uitgebreide Turaev-Viro teorie ontwikkel deur Balsam en Kirillov binne die bikategoriese voorbringer-en-verwantskap raamwerk, en gebruik dit om te bewys dat die string-net en Turaev-Viro 123-TKVTe ekwivalent is. Doctoral 2018-01-26T06:36:36Z 2018-04-09T06:52:46Z 2018-01-26T06:36:36Z 2018-04-09T06:52:46Z 2018-03 Thesis http://hdl.handle.net/10019.1/103324 en_ZA Stellenbosch University vii, 139 pages : illustrations (chiefly colour) application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | String nets (Mathematics) UCTD Quantum field theories Turaev-Viro theory State space (Mathematics) Goosen, Gerrit Oriented 123-TQFTs via String-Nets and State-Sums |
| title | Oriented 123-TQFTs via String-Nets and State-Sums |
| title_full | Oriented 123-TQFTs via String-Nets and State-Sums |
| title_fullStr | Oriented 123-TQFTs via String-Nets and State-Sums |
| title_full_unstemmed | Oriented 123-TQFTs via String-Nets and State-Sums |
| title_short | Oriented 123-TQFTs via String-Nets and State-Sums |
| title_sort | oriented 123 tqfts via string nets and state sums |
| topic | String nets (Mathematics) UCTD Quantum field theories Turaev-Viro theory State space (Mathematics) |
| url | http://hdl.handle.net/10019.1/103324 |
| work_keys_str_mv | AT goosengerrit oriented123tqftsviastringnetsandstatesums |