Some differentials on Khovanov-Rozansky homology

Abstract

We study the relationship between the HOMFLY and sl(N) knot homologies introduced by Khovanov and Rozansky. For each N>0, we show there is a spectral sequence which starts at the HOMFLY homology and converges to the sl(N) homology. As an application, we determine the KR-homology of knots with 9 crossings or fewer.

55 pages, 18 figures. v2: Corrected gradings in the statement of proposition 7.6