We prove that the full twist is a Serre functor in the homotopy category of type A Soergel bimodules. As a consequence, we relate the top and bottom Hochschild degrees in Khovanov-Rozansky homology, categorifying a theorem of Kálmán.

No abstract

We show, using Mellit's recent results, that Kálmán's full twist formula for the HOMFLY polynomial can be generalized to a formula for superpolynomials in the case of positive toric braids.

No abstract

We give an algorithm to compute the reduced HOMFLY homology for knots. We determine the homologies for 695 prime knots, including all prime knots with up to 10 crossings, and all prime knots with 11 crossings and braid length up to 13.