{
  "abstract": "We present a new diagrammatic construction of Lagrangian surfaces in all symplectic toric $4$-manifolds from objects called multi-grid diagrams. These are a generalisation of triple grid diagrams for Lagrangian surfaces in $\\mathbb{CP}^2$ wherein the underlying trisection is replaced by the more general notion of a toric decomposition. We give examples of multi-grid diagrams for Lagrangian surfaces in a range of symplectic toric $4$-manifolds, including Evans' recent non-squeezable Klein bottle in $S^2 \\times S^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42076",
  "author_total": 2,
  "authors": [
    {
      "name": "Shintaro Fushida-Hardy"
    },
    {
      "name": "Laura Wakelin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2d0gpkb6ceqwk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42076",
  "fulltext_url": null,
  "id": "2d0gpkb6ceqwk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42076",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42076",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2d0gpkb6ceqwk.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42076",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42076"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Constructing Lagrangian surfaces in all symplectic toric $4$-manifolds from multi-grid diagrams",
  "title_text": "Constructing Lagrangian surfaces in all symplectic toric $4$-manifolds from multi-grid diagrams",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/2d0gpkb6ceqwk",
  "venue": "arXiv",
  "versions": []
}