In this thesis we study Khovanov homology, a link invariant in the form of a omology theory of which the graded Euler characteristic is precisely the Jones polynomial. It is a remarkable homological link invariant as it has a combinatorial description and can be computed by an algorithm that mimics Louis Kauffman’s state model formulation of the Jones polynomial. Moreover, Khovanov homology has been shown to be strictly stronger than the Jones polynomial, proving its inherent value as a link invariant. Khovanov homology also has an extension to tangles which simultaneously categorifies the extension of the Jones polynomial to tangles.
| Datum prijs | 30 jun. 2022 |
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| Originele taal | English |
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An exploration of Khovanov Homology
Van Rooy, E. E. ((PhD) Student), Van den Bergh, M. (Promotor), Vercruysse, J. (Jury), Raedschelders, T. (Jury). 30 jun. 2022
Scriptie/Masterproef: Master's Thesis