Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory

Kokoro Tanaka

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Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory

Kokoro Tanaka

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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 {\it Khovanov-Jacobsson number}, by considering the surface-knot as a link cobordism between empty links. In this paper, we define an invariant of a surface-knot which is a generalization of the Khovanov-Jacobsson number by using Bar-Natan's theory, and prove that any $T^2$-knot has the trivial Khovanov-Jacobsson number.

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BibTeX RIS

Kokoro Tanaka. 2005-02-27. Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory. https://arxiv.org/abs/math/0502371

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