{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Turaev-Viro theory as an extended \nTQFT","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/1951/59574"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"In recent years, \nthe application of quantum groups to the study of low-dimensional topology has become an active topic of research. In \nthree-dimensions, these yield the well-known Reshetihkin-Turaev (RT) invariants, which are a mathematical formulation \nof Chern- Simons theory and Turaev-Viro (TV) theory, which is a convergent form of the Ponzano-Regge state sum \nformula from Quantum Gravity. Both RT and TV are more than invariants;they have a far richer structure known as a \nTopological Quantum Field Theory (TQFT). We describe Turaev-Viro theory as an extended (3-2-1)-TQFT and use this \ndescription to prove a theorem relating it to RT theory. Turaev-Viro theory has several equivalent descriptions. We \nexamine Kitaev's toric code from quantum computation and the Levin- Wen model from condensed matter physics and \nshow that these theories are extended TQFTs coinciding with TV theory."},{"label":"dcterms.available","value":"2015-04-24T14:46:11Z"},{"label":"dcterms.contributor","value":"Kirillov Jr., \nAlexander"},{"label":"dcterms.creator","value":"Balsam, Benjamin"},{"label":"dcterms.dateAccepted","value":"2015-04-24T14:46:11Z"},{"label":"dcterms.dateSubmitted","value":"2015-04-24T14:46:11Z"},{"label":"dcterms.description","value":"Department of Mathematics"},{"label":"dcterms.extent","value":"192 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/1951/59574"},{"label":"dcterms.issued","value":"2012-08-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2013-05-22T17:34:07Z (GMT). No. of bitstreams: 1\nBalsam_grad.sunysb_0771E_11015.pdf: 1297910 bytes, checksum: 13a91fb5b82867761a9d37aab22ee368 (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Mathematics--Physics"},{"label":"dcterms.title","value":"Turaev-Viro theory as an extended \nTQFT"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/16%2F06%2F70%2F160670352785652068980298365144213659355/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/16%2F06%2F70%2F160670352785652068980298365144213659355","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}