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

References in corpus (7)

• Khovanov's homology for tangles and cobordisms
• Heegaard Floer homology and alternating knots
• Khovanov-Rozansky Homology and Topological Strings
• Note on Khovanov link cohomology
• The support of the Khovanov's invariants for alternating knots
• Triply-graded link homology and Hochschild homology of Soergel bimodules
• Khovanov-Rozansky homology of two-bridge knots and links

Cited by in corpus (30)

• Knot Homology from Refined Chern-Simons Theory
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Knot homology groups from instantons
• Diagrammatics for Soergel categories
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• DAHA and iterated torus knots
• Colored Kauffman Homology and Super-A-polynomials
• Rasmussen's spectral sequences and the sl(N)-concordance invariants
• Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial
• A note on Gornik's perturbation of Khovanov-Rozansky homology
• Refined Chern-Simons Theory and Knot Homology
• Generic deformations of the colored sl(N)-homology for links
• Equivariant colored sl(N)-homology for links
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Matrix factorizations and intertwiners of the fundamental representations of quantum group U_q (sl_n)
• sl3-foam homology calculations
• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Matrix factorizations and colored MOY graphs
• q,t-Catalan numbers and knot homology
• On stable Khovanov homology of torus knots
• Rouquier Complexes are Functorial over Braid Cobordisms
• The diagrammatic Soergel category and sl(2) and sl(3) foams
• Integral HOMFLY-PT and sl(n)-link homology
• Wall-Crossing Morphisms in Khovanov-Rozansky Homology
• Colored Morton-Franks-Williams inequalities
• Matrix factorizations and double line in ${\mathfrak{sl}}_n$ quantum link invariant
• A categorification of the quantum sl(N)-link polynomials using foams
• Khovanov-Rozansky homology and Directed Cycles
• The 1,2-coloured HOMFLY-PT link homology