Torus knots in Lens spaces, open Gromov-Witten invariants, and topological recursion

2023/06/08 by Jinghao Yu, Yu, Jinghao, Zhengyu Zong +1
Mathematics · Medicine · #Algebraic Geometry (math.AG) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2306.05326

openalex publication_date 2023/06/08 · openalex created_date 2023/06/10 · openalex updated_date 2026/07/28

Abstract

Starting from a torus knot K in the lens space L(p,-1), we construct a Lagrangian sub-manifold L_K in X=(O_ℙ¹(-1)⊕ O_ℙ¹(-1))/ℤ_p under the conifold transition. We prove a mirror theorem which relates the all genus open-closed Gromov-Witten invariants of (X,L_K) to the topological recursion on the B-model spectral curve. This verifies a conjecture in \citeBor-Bri in the case of lens space.

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