| dc.identifier.uri | http://hdl.handle.net/1951/59913 | |
| dc.identifier.uri | http://hdl.handle.net/11401/71455 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | 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> × 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. | |
| dcterms.available | 2013-05-22T17:35:47Z | |
| dcterms.available | 2015-04-24T14:47:37Z | |
| dcterms.contributor | Kirillov, Alexander | en_US |
| dcterms.contributor | Viro, Oleg | en_US |
| dcterms.contributor | Plamenevskaya, Olga | en_US |
| dcterms.contributor | Shumakovitch, Alexander. | en_US |
| dcterms.creator | Weng, Luoying | |
| dcterms.dateAccepted | 2013-05-22T17:35:47Z | |
| dcterms.dateAccepted | 2015-04-24T14:47:37Z | |
| dcterms.dateSubmitted | 2013-05-22T17:35:47Z | |
| dcterms.dateSubmitted | 2015-04-24T14:47:37Z | |
| dcterms.description | Department of Mathematics | en_US |
| dcterms.extent | 127 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/1951/59913 | |
| dcterms.identifier | Weng_grad.sunysb_0771E_10789 | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/71455 | |
| dcterms.issued | 2011-12-01 | |
| dcterms.language | en_US | |
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| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Mathematics | |
| dcterms.subject | functoriality, immersed, Isotopy invariant, Khovanov, TQFT | |
| dcterms.title | Isotopy Invaraints of Immersed surfaces in a 4-manifold | |
| dcterms.type | Dissertation | |
