Skein recursion for holomorphic curves and invariants of the unknot

2020/12/30 by Tobias Ekholm, Vivek Shende, Ekholm, Tobias +1 · 3 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Computational Geometry and Mesh Generation #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Polynomial and algebraic computation #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2012.15366

openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the skein-valued Gromov-Witten partition function for a single toric Lagrangian brane in ℂ³ 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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