The Kanenobu knots and Khovanov-Rozansky homology

Abstract

Kanenobu has given infinite families of knots with the same HOMFLYPT polynomials. We show that these knots also have the same s l ( n ) 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.