{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Isotopy Invaraints of Immersed surfaces in a 4-manifold","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/1951/59913"},{"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 this this dissertation we introduce an isotopy invariant of generically immersed surfaces in some 4-manifold. The construction is based on Khovanov homology and its variants in the same way as the construction of Turaev-Viro module of a 3-manifold with infinite cyclic covering relies on TQFT. The invariant is first constructed for generically immersed surfaces in S<super>3</super> &times S<super>1</super> using the functoriality of Khovanov homology, and is generalized by using new versions of Khovanov homology. Moreover, it is also generalized to surfaces generically immersed transversal to a standardly embedded S<super>2</super> in S<super>4</super>. Examples are studied to illustrate the strength and weakness of this invariant."},{"label":"dcterms.available","value":"2013-05-22T17:35:47Z"},{"label":"dcterms.contributor","value":"Shumakovitch, Alexander."},{"label":"dcterms.creator","value":"Weng, Luoying"},{"label":"dcterms.dateAccepted","value":"2013-05-22T17:35:47Z"},{"label":"dcterms.dateSubmitted","value":"2015-04-24T14:47:37Z"},{"label":"dcterms.description","value":"Department of Mathematics"},{"label":"dcterms.extent","value":"127 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"Weng_grad.sunysb_0771E_10789"},{"label":"dcterms.issued","value":"2011-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2013-05-22T17:35:47Z (GMT). No. of bitstreams: 1\nWeng_grad.sunysb_0771E_10789.pdf: 980145 bytes, checksum: cf616b8be20d1a62b30a351fda9da52a (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"functoriality, immersed, Isotopy invariant, Khovanov, TQFT"},{"label":"dcterms.title","value":"Isotopy Invaraints of Immersed surfaces in a 4-manifold"},{"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/2/44%2F67%2F10%2F44671092324652934875285839349613930662/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/2/44%2F67%2F10%2F44671092324652934875285839349613930662","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}