{
  "abstract": "We associate to each compact subset $K$ of a closed symplectic manifold $M$ an $A_\\infty$-category $\\Fuk_K$, called the Fukaya category with support on $K$. The objects are tautologically unobstructed global Lagrangians endowed with appropriate decorations. The dependence on $K$ is detected by the morphism complexes which can be computed by completed telescopes associated with acceleration data for $K$. In particular, these vanish for Lagrangians disjoint of $K$. For $K=M$ this recovers the usual Fukaya category of tautologically unobstructed objects. These categories admit restriction functors under inclusions of compact subsets. We prove a Mayer--Vietoris descent theorem for weakly involutive covers. The construction is carried out over the Novikov ring and is established whenever classical transversality methods apply.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35565",
  "author_total": 3,
  "authors": [
    {
      "name": "Mohammed Abouzaid"
    },
    {
      "name": "Yoel Groman"
    },
    {
      "name": "Umut Varolgunes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de2geyfvf4vpf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35565",
  "fulltext_url": null,
  "id": "de2geyfvf4vpf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35565",
  "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.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214730752",
  "pdf_url": "https://arxiv.org/pdf/2609.35565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de2geyfvf4vpf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35565"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fukaya category with supports",
  "title_text": "Fukaya category with supports",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/de2geyfvf4vpf",
  "venue": "arXiv",
  "versions": []
}