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http://dx.doi.org/10.4134/BKMS.b141003

A RECURSIVE FORMULA FOR THE KHOVANOV COHOMOLOGY OF KANENOBU KNOTS  

Lei, Fengchun (School of Mathematical Sciences Dalian University of Technology)
Zhang, Meili (Department of Basis Dalian Naval Academy)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 1-15 More about this Journal
Abstract
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.
Keywords
homologically thin knot; Jones polynomial; signature; Kanenobu knots; Khovanov cohomology; odd Khovanov homology;
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