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

2005/02/17 by Kokoro Tanaka, Tanaka, Kokoro · 1 citation
Engineering · Mathematics · #Adhesion, Friction, and Surface Interactions #Advanced Materials and Mechanics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Primary 57Q45 #Quantum Algebra (math.QA) #Secondary 57M25 #math.GT #math.QA #msc:57M25 #msc:57Q45

paper · pdf · doi:10.48550/arxiv.math/0502371

7 pages, a comment on Corollary 1.2 is added

openalex publication_date 2005/02/17 · arxiv created 2005/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \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 T²-knot has the trivial Khovanov-Jacobsson number.

Citations

• An endomorphism of the Khovanov invariant

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• Lecture notes on link homologies and knotted surfaces

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