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 A recursive formula for the Khovanov cohomology of Kanenobu knots Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 1-15 https://doi.org/10.4134/BKMS.b141003Published online December 21, 2016Printed January 31, 2017 Fengchun Lei and Meili Zhang Dalian University of Technology, Dalian Naval Academy 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 MSC numbers : 57M25, 57M27 Downloads: Full-text PDF