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arXiv · 2012.15366

Skein recursion for holomorphic curves and invariants of the unknot

Tobias Ekholm·Vivek Shende
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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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Tobias Ekholm, Vivek Shende. 2020-12-30. Skein recursion for holomorphic curves and invariants of the unknot. https://arxiv.org/abs/2012.15366

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