Oriented 123-TQFTs via String-Nets and State-Sums
| dc.contributor.advisor | Bartlett, Bruce | en_ZA |
| dc.contributor.author | Goosen, Gerrit | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. | en_ZA |
| dc.date.accessioned | 2018-01-26T06:36:36Z | |
| dc.date.accessioned | 2018-04-09T06:52:46Z | |
| dc.date.available | 2018-01-26T06:36:36Z | |
| dc.date.available | 2018-04-09T06:52:46Z | |
| dc.date.issued | 2018-03 | |
| dc.description | Thesis (PhD)--Stellenbosch University, 2018. | en_ZA |
| dc.description.abstract | 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. | en_ZA |
| dc.description.abstract | 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. | af_ZA |
| dc.format.extent | vii, 139 pages : illustrations (chiefly colour) | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/10019.1/103324 | |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | en_ZA |
| dc.subject | String nets (Mathematics) | en_ZA |
| dc.subject | UCTD | en_ZA |
| dc.subject | Quantum field theories | en_ZA |
| dc.subject | Turaev-Viro theory | en_ZA |
| dc.subject | State space (Mathematics) | en_ZA |
| dc.title | Oriented 123-TQFTs via String-Nets and State-Sums | en_ZA |
| dc.type | Thesis | en_ZA |