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

DOI:
https://doi.org/10.1090/S0002-9939-06-08397-3

Published electronically:
May 18, 2006

MathSciNet review:
2240683

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Kokoro Tanaka**

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

Email:
k-tanaka@ms.u-tokyo.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-06-08397-3

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.