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HOMFLYPT homology of Coxeter links

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arxiv 1706.00124 v3 pith:FWNTDVLV submitted 2017-05-31 math.AG math.GT

Alexei Oblomkov , Lev Rozansky This is my paper · ORCID
classification math.AGmath.GT
keywords coxeterlinkshomologylinkproducttorusbraidsbundle
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abstract

A Coxeter link is a closure of a product of two braids, one being a quasi-Coxeter element and the other being a product of partial full twists. This class of links includes torus knots \(T_{n,k}\) and torus links \(T_{n,nk}\). We identify the knot homology of a Coxeter link with the space of sections of a particular line bundle on a natural generalization of the punctual locus inside the flag Hilbert scheme of points in \(\mathbb{C}^2\).

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  1. Instanton slices and their superpolynomials

    math.AG 2026-07 conditional novelty 7.0 of 10

    Motivic superpolynomials of plane-curve singularities are repackaged as "instanton slice" counts, conjecturally matching new DAHA superpolynomials that are claimed to produce superpolynomials for hyperbolic knots.

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