{"paper":{"title":"Torus knots in Lens spaces, open Gromov-Witten invariants, and topological recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.AG","authors_text":"Jinghao Yu, Zhengyu Zong","submitted_at":"2023-06-08T16:20:46Z","abstract_excerpt":"Starting from a torus knot $\\mathcal{K}$ in the lens space $L(p,-1)$, we construct a Lagrangian sub-manifold $L_{\\mathcal{K}}$ in $\\mathcal{X}=\\big(\\mathcal{O}_{\\mathbb{P}^1}(-1)\\oplus \\mathcal{O}_{\\mathbb{P}^1}(-1)\\big)/\\mathbb{Z}_p$ under the conifold transition. We prove a mirror theorem which relates the all genus open-closed Gromov-Witten invariants of $(\\mathcal{X},L_{\\mathcal{K}})$ to the topological recursion on the B-model spectral curve. This verifies a conjecture in \\cite{Bor-Bri} in the case of lens space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05326","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.05326/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}