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Serre duality for Khovanov-Rozansky homology

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arxiv 1902.08281 v2 pith:S4ZJLQAS submitted 2019-02-21 math.RT math.GT

Eugene Gorsky , Matthew Hogancamp , Anton Mellit , Keita Nakagane This is my paper · ORCID
classification math.RTmath.GT
keywords homologykhovanov-rozanskyserrebimodulesbottomcategorifyingcategoryconsequence
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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 K\'alm\'an.

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  1. Torus link homology

    math.GT 2019-09 conditional novelty 6.0 of 10

    Positive torus links T(m,n) and Sym^l-colored torus knots have triply graded Khovanov-Rozansky homology equal to an explicitly defined family of polynomials p(v,w).

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