Mathematics – Geometric Topology
Scientific paper
2005-02-17
Mathematics
Geometric Topology
7 pages, a comment on Corollary 1.2 is added
Scientific paper
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.
No associations
LandOfFree
Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-97448