State sums in two dimensional fully extended topological field theories
| dc.contributor.advisor | Freed, Daniel S. | en |
| dc.contributor.committeeMember | Ben-Zvi, David | en |
| dc.contributor.committeeMember | Distler, Jacques | en |
| dc.contributor.committeeMember | Reid, Alan | en |
| dc.contributor.committeeMember | Rodriguez-Villegas, Fernando | en |
| dc.creator | Davidovich, Orit | en |
| dc.date.accessioned | 2011-06-01T14:15:32Z | en |
| dc.date.accessioned | 2011-06-01T14:15:40Z | en |
| dc.date.accessioned | 2017-05-11T22:22:03Z | |
| dc.date.available | 2011-06-01T14:15:32Z | en |
| dc.date.available | 2011-06-01T14:15:40Z | en |
| dc.date.available | 2017-05-11T22:22:03Z | |
| dc.date.issued | 2011-05 | en |
| dc.date.submitted | May 2011 | en |
| dc.date.updated | 2011-06-01T14:15:40Z | en |
| dc.description | text | en |
| dc.description.abstract | A state sum is an expression approximating the partition function of a d-dimensional field theory on a closed d-manifold from a triangulation of that manifold. To consider state sums in completely local 2-dimensional topological field theories (TFT's), we introduce a mechanism for incorporating triangulations of surfaces into the cobordism ([infinity],2)-category. This serves to produce a state sum formula for any fully extended 2-dimensional TFT possibly with extra structure. We then follow the Cobordism Hypothesis in classifying fully extended 2-dimensional G-equivariant TFT's for a finite group G. These are oriented theories in which bordisms are equipped with principal G-bundles. Combining the mechanism mentioned above with our classification results, we derive Turaev's state sum formula for such theories. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/2152/ETD-UT-2011-05-3139 | en |
| dc.language.iso | eng | en |
| dc.subject | Topology | en |
| dc.subject | Topological field theory | en |
| dc.subject | Quantum field theory | en |
| dc.subject | Cobordism hypothesis | en |
| dc.subject | Cobordism theory | en |
| dc.subject | State sum | en |
| dc.subject | G-equivariant theory | en |
| dc.subject | Bordism category | en |
| dc.subject | Algebraic topology | en |
| dc.title | State sums in two dimensional fully extended topological field theories | en |
| dc.type.genre | thesis | en |