Homology of torus knots

Abstract

Using the method of Elias and Hogancamp and combinatorics of toric braids from our proof of the rational shuffle conjecture, we give an explicit formula for the triply graded Khovanov–Rozansky homology (superpolynomial) of an arbitrary positive torus knot, thereby proving some of the conjectures of Aganagic and Shakirov, Cherednik, Gorsky and Negut, and Oblomkov, Rasmussen and Shende.