Homology of torus knots

Abstract

Using the method of Elias-Hogancamp and combinatorics of toric braids we give an explicit formula for the triply graded Khovanov-Rozansky homology of an arbitrary torus knot, thereby proving some of the conjectures of Aganagic-Shakirov, Cherednik, Gorsky-Negut and Oblomkov-Rasmussen-Shende.

References in corpus (1)

• Khovanov-Rozansky homology and higher Catalan sequences

Cited by in corpus (15)

• Hilbert schemes and $y$-ification of Khovanov-Rozansky homology
• Hopf dreams and diagonal harmonics
• Torus link homology
• The action of full twist on the superpolynomial for torus knots
• Modules over plane curve singularities in any ranks and DAHA
• Colored Khovanov-Rozansky homology for infinite braids
• Tautological classes and symmetry in Khovanov-Rozansky homology
• Soergel bimodules and matrix factorizations
• $(G{L}_k\times S_n)$-Modules of Multivariate Diagonal Harmonics
• Structures in HOMFLY-PT homology
• Curved Rickard complexes and link homologies
• A categorification of the colored Jones polynomial at a root of unity
• Ext-enhanced monoidal Koszul duality for ${\mathrm{GL}}_2$
• Link splitting deformation of colored Khovanov--Rozansky homology
• Algebra and geometry of link homology