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Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory
Author(s):
Kokoro
Tanaka
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3685-3689.
MSC (2000):
Primary 57Q45;
Secondary 57M25
Posted:
May 18, 2006
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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.
References:
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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:
10.1090/S0002-9939-06-08397-3
PII:
S 0002-9939(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
Posted:
May 18, 2006
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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