{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Representation Theory of Categorified Quantum sl2","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/11401/71178"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"Quantum sl2 gives rise to the Jones polynomial knot invariant. One of the insights of categorification is that this 3-dimensional picture is a shadow, the decategorification, of a 4-dimensional picture. Thus, the categorification of quantum sl2 gives rise through its representation theory to Khovanov homology, the categorification of the Jones polynomial. In the 3-dimensional picture, the algebra of Temperley-Lieb diagrams, used in the construction of the Jones polynomial, gives a graphical calculus for intertwiners of the representations of quantum sl2. We show that the algebra of Bar-Natan's dotted cobordisms, used in the construction of Khovanov homology, gives a graphical calculus for intertwiners of representations of categorified quantum sl2."},{"label":"dcterms.available","value":"2015-04-24T14:46:18Z"},{"label":"dcterms.contributor","value":"Viro, Oleg."},{"label":"dcterms.creator","value":"Chatav, Eitan"},{"label":"dcterms.dateAccepted","value":"2013-05-22T17:34:18Z"},{"label":"dcterms.dateSubmitted","value":"2013-05-22T17:34:18Z"},{"label":"dcterms.description","value":"Department of Mathematics"},{"label":"dcterms.extent","value":"54 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/71178"},{"label":"dcterms.issued","value":"2012-08-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2015-04-24T14:46:18Z (GMT). No. of bitstreams: 3\nChatav_grad.sunysb_0771E_11132.pdf.jpg: 1894 bytes, checksum: a6009c46e6ec8251b348085684cba80d (MD5)\nChatav_grad.sunysb_0771E_11132.pdf.txt: 53018 bytes, checksum: 603222e1a398474f766c356a0eeb010b (MD5)\nChatav_grad.sunysb_0771E_11132.pdf: 498700 bytes, checksum: 88043f88112e1d162f27eda37ebaeede (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Algebra, Categorification, Homology, Quantum, Representation Theory, Topology"},{"label":"dcterms.title","value":"Representation Theory of Categorified Quantum sl2"},{"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/2/12%2F93%2F25%2F129325902472267840896544700945414510131/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/2/12%2F93%2F25%2F129325902472267840896544700945414510131","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}