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Homology of torus knots

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arxiv 1704.07630 v1 pith:Q3272ILH submitted 2017-04-25 math.QA math.AGmath.GTmath.RT

Anton Mellit This is my paper · ORCID
classification math.QAmath.AGmath.GTmath.RT
keywords homologytorusaganagic-shakirovarbitrarybraidscherednikcombinatoricsconjectures
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Using the method of Elias-Hogancamp and combinatorics of toric braids we give an explicit formula for the triply graded Khovanov-Rozansky homology of an arbitrary torus knot, thereby proving some of the conjectures of Aganagic-Shakirov, Cherednik, Gorsky-Negut and Oblomkov-Rasmussen-Shende.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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).

  2. Recursions for rational q,t-Catalan numbers

    math.CO 2019-08 conditional novelty 6.0 of 10

    A fixed-length binary-sequence recursion computes rational q,t-Catalan power series and matches the Hogancamp-Mellit recursion, confirming the link to Khovanov-Rozansky homology.

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