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

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dc.creatorTanaka, Kokoro
dc.date2005-02-17
dc.date2005-02-27
dc.date.accessioned2026-07-07T05:17:06Z
dc.date.available2026-07-07T05:17:06Z
dc.descriptionKhovanov 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.
dc.description7 pages, a comment on Corollary 1.2 is added
dc.identifierhttps://arxiv.org/abs/math/0502371
dc.identifierhttp://arxiv.org/abs/math/0502371
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74229
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subjectPrimary 57Q45; Secondary 57M25
dc.titleKhovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory
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