q,t-Catalan numbers and knot homology

Abstract

We propose an algebraic model of the conjectural triply graded homology of Gukov, Dunfield and Rasmussen for some torus knots. It turns out to be related to the q,t-Catalan numbers of Garsia and Haiman.

Revised version, more examples added

References in corpus (2)

• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Some differentials on Khovanov-Rozansky homology

Cited by in corpus (9)

• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial
• Khovanov-Rozansky homology and higher Catalan sequences
• Compactified Jacobians and q,t-Catalan Numbers, I
• Torus knot polynomials and susy Wilson loops
• Torus link homology
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• On stable Khovanov homology of torus knots
• Soergel bimodules and matrix factorizations