Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory |
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Authors: | Kokoro Tanaka |
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Affiliation: | Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan |
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Abstract: | Khovanov introduced a cohomology theory for oriented classical links whose graded Euler characteristic is the Jones polynomial. Since Khovanov's theory is functorial for link cobordisms between classical links, we obtain an invariant of a surface-knot, called the Khovanov-Jacobsson number, by considering the surface-knot as a link cobordism between empty links. In this paper, we study an extension of the Khovanov-Jacobsson number derived from Bar-Natan's theory, and prove that any -knot has trivial Khovanov-Jacobsson number. |
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Keywords: | Khovanov cohomology surface-knot Khovanov-Jacobsson number |
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