{
  "abstract": "Let $X$ be a toric Fano surface. Let $π: \\widehat{X} \\rightarrow X$ be a toric blow up at a point. We use the Topological Vertex [AKMV] to prove a higher genus, higher winding, open-closed duality between the toric Calabi-Yau 3-folds $K_X, K_{\\widehat{X}}$. For $g \\geq 0, w \\geq 1$, we show the equality $n_g(K_{\\widehat{X}}, π^*β- wC) = (-1)^g N_{g, (w)}^{LMOV}(K_X/L, β)$, where $n_g(K_{\\widehat{X}}, π^*β- wC)$ is the genus-$g$, Gopakumar-Vafa invariant of $K_{\\widehat{X}}$ in curve class $π^*β-wC$, where $β\\in H_2(X, \\mathbb{Z})$ and $C$ is the exceptional curve, and $N_{g, (w)}^{LMOV}(K_X/L, β)$ is the genus-$g$, LMOV invariant of an outer Aganagic-Vafa brane $L \\subset K_X$ in class $β$ and representation $(w)$, or the Young Tableau of a single row with $w$ boxes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05926",
  "author_total": 1,
  "authors": [
    {
      "name": "Benjamin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11x7q62wb50m5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05926",
  "fulltext_url": null,
  "id": "11x7q62wb50m5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05926",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212032958",
  "pdf_url": "https://arxiv.org/pdf/2609.05926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11x7q62wb50m5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.05926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05926"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Open-closed duality in higher genus and winding",
  "title_text": "Open-closed duality in higher genus and winding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/11x7q62wb50m5",
  "venue": "arXiv",
  "versions": []
}