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On stable sl3-homology of torus knots (1404.0623v1)
Published 2 Apr 2014 in math.GT, math.AC, math.QA, and math.RT
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.