CEU Electronic Theses and Dissertations, 2018
| Author | Yozgyur, Ramazan |
|---|---|
| Title | Introduction to Khovanov homology |
| Summary | In this thesis, we study the definition of Khovanov homology. Before doing that, we describe some basic information about knot theory and homological algebra, which we need in the definition of Khovanov homology. We also describe the definition of the unnormalized Jones polynomial of a knot or link and then extend this construction (based on the paper of Bar Natan) to the definition of Khovanov homology. We describe the detailed definition of Khovanov homology, as a bigraded vector space invariant of a link, which has the unnormalized Jones polynomial as its Euler characteristic. Moreover, we study slice genus via Khovanov homology. We study new knot invariant to study slice genus and prove main theorems about slice genus. At the last chapter, we study the relation of Khovanov homology and topological quantum field theory |
| Supervisor | Stipsicz Andras |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2018/ozgur_ramazan.pdf |
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