The Kanenobu knots and Khovanov-Rozansky homology

Lobb, Andrew

doi:10.1090/S0002-9939-2014-11863-6

The Kanenobu knots and Khovanov-Rozansky homology
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Proc. Amer. Math. Soc. 142 (2014), 1447-1455 Request permission

Abstract:

Kanenobu has given infinite families of knots with the same HOMFLYPT polynomials. We show that these knots also have the same $sl(n)$ and HOMFLYPT homologies, thus giving the first example of an infinite family of knots indistinguishable by these invariants. This is a consequence of a structure theorem about the homologies of knots obtained by twisting up the ribbon of a ribbon knot with one ribbon.

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