• 제목/요약/키워드: Khovanov cohomology

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A RECURSIVE FORMULA FOR THE KHOVANOV COHOMOLOGY OF KANENOBU KNOTS

  • Lei, Fengchun;Zhang, Meili
    • 대한수학회보
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    • 제54권1호
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    • pp.1-15
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    • 2017
  • Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.