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

Author: Kokoro Tanaka
Journal: Proc. Amer. Math. Soc. 134 (2006), 3685-3689
MSC (2000): Primary 57Q45; Secondary 57M25
Published electronically: May 18, 2006
MathSciNet review: 2240683
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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 $ T^2$-knot has trivial Khovanov-Jacobsson number.

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Kokoro Tanaka
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan

Keywords: Khovanov cohomology, surface-knot, Khovanov-Jacobsson number
Received by editor(s): March 14, 2005
Received by editor(s) in revised form: June 14, 2005
Published electronically: May 18, 2006
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.