Type
Text
Type
Dissertation
Advisor
Viro, Oleg | Kirillov, Alexander | Plamenevskaya, Olga | Shumakovitch, Alexander.
Date
2011-12-01
Keywords
Mathematics | functoriality, immersed, Isotopy invariant, Khovanov, TQFT
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71455
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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 S3 × S1 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 S2 in S4. Examples are studied to illustrate the strength and weakness of this invariant. | 127 pages
Recommended Citation
Weng, Luoying, "Isotopy Invaraints of Immersed surfaces in a 4-manifold" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 661.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/661