An endomorphism of the Khovanov invariant

2002/10/15 by Eun Soo Lee, Lee, Eun Soo · 4 citations
Computer Science · Mathematics · #57M27 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0210213

To appear in Adv. Math.; Brief summary of Khovanov invariant (math.QA/9908171) and previous result of the author (math.GT/0201105) added

openalex publication_date 2002/10/15 · arxiv created 2004/10/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is determined by its Jones polynomial, signature, and the linking numbers of its components.

Cited by

• Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory
• Step by step categorification of the Jones polynomial in Kauffman's version
• Khovanov-Kauffman Homology for embedded Graphs
• Khovano Homology and Embedded Graphs

Related

• The support of the Khovanov's invariants for alternating knots
• A generalized skein relation for Khovanov homology and a categorification of the θ-invariant
• Contributions to Khovanov Homology
• Torsion in Khovanov homology of homologically thin knots
• The Khovanov homology of alternating virtual links