Skein recursion for holomorphic curves and invariants of the unknot

Tobias Ekholm; Vivek Shende

Skein recursion for holomorphic curves and invariants of the unknot

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arxiv 2012.15366 v1 pith:AATYMKM4 submitted 2020-12-30 math.SG hep-thmath.GTmath.QA

Tobias Ekholm , Vivek Shende This is my paper · ORCID

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keywords recursionequationskein-valuedbranecertainconifoldcurvecurves

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abstract

We determine the skein-valued Gromov-Witten partition function for a single toric Lagrangian brane in $\mathbb{C}^3$ or the resolved conifold. We first show geometrically they must satisfy a certain skein-theoretic recursion, and then solve this equation. The recursion is a skein-valued quantization of the equation of the mirror curve. The solution is the expected hook-content formula.

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