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<p>Starting from a torus knot <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\cal{K}\)</EquationSource> </InlineEquation> in the lens space <i>L</i>(<i>p</i>, −1), we construct a Lagrangian sub-manifold <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_{\cal{K}}\)</EquationSource> </InlineEquation> in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\cal{X}}=({\cal{O}}_{\mathbb{P}^1}(-1)\oplus {\cal{O}}_{\mathbb{P}^1}(-1))/\mathbb{Z}_{p}\)</EquationSource> </InlineEquation> under the conifold transition. We prove a mirror theorem which relates all genus open-closed Gromov-Witten invariants of (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\cal{X}}, L_{\cal{K}}\)</EquationSource> </InlineEquation>) to the topological recursion on the B-model spectral curve. This verifies a conjecture by Borot and Brini (2018) in the case of the lens space.</p>

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

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Jinghao Yu,
  • Zhengyu Zong

摘要

Starting from a torus knot \(\cal{K}\) in the lens space L(p, −1), we construct a Lagrangian sub-manifold \(L_{\cal{K}}\) in \({\cal{X}}=({\cal{O}}_{\mathbb{P}^1}(-1)\oplus {\cal{O}}_{\mathbb{P}^1}(-1))/\mathbb{Z}_{p}\) under the conifold transition. We prove a mirror theorem which relates all genus open-closed Gromov-Witten invariants of ( \({\cal{X}}, L_{\cal{K}}\) ) to the topological recursion on the B-model spectral curve. This verifies a conjecture by Borot and Brini (2018) in the case of the lens space.