On stable sl3-homology of torus knots

Abstract

The stable Khovanov-Rozansky homology of torus knots has been conjecturally described as the Koszul homology of an explicit non-regular sequence of polynomials. We verify this conjecture against newly available computational data for sl(3)-homology. Special attention is paid to torsion. In addition, explicit conjectural formulae are given for the sl(N)-homology of (3,m)-torus knots for all N and m, which are motivated by higher categorified Jones-Wenzl projectors. Structurally similar formulae are proven for Heegard-Floer homology.

16 pages, 3 tables

References in corpus (5)

• Torus knots and the rational DAHA
• Torsion in Khovanov homology of semi-adequate links
• Clasp technology to knot homology via the affine Grassmannian
• An Exceptional Collection For Khovanov Homology
• sl3-foam homology calculations

Cited by in corpus (5)

• On colored HOMFLY polynomials for twist knots
• Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?
• A hitchhiker's guide to Khovanov homology
• A family of ${\mathfrak{sl}}_n$-like invariants in knot Floer homology
• Towards formalization of the soliton counting technique for the Khovanov-Rozansky invariants in the deformed $\mathcal{R}$-matrix approach