The Kanenobu knots and Khovanov-Rozansky homology

Details The Kanenobu knots and Khovanov-Rozansky homology The Kanenobu knots and Khovanov-Rozansky homology

2011-05-19

arxiv.org/abs/1105.3985v1

Mathematics

Geometric Topology

9 pages, 6 figures

Scientific paper

Kanenobu has given infinite families of knots with the same HOMFLY polynomials. We show that these knots also have the same sl(n) and HOMFLY homologies, thus giving the first example of an infinite family of knots undistinguishable 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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