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

Kokoro Tanaka
2006 Proceedings of the American Mathematical Society  
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.
doi:10.1090/s0002-9939-06-08397-3 fatcat:5pm5mcsoabewjm4sslpkrrg6ka