{
  "abstract": "For an odd prime $p$, we prove a Smith inequality over $\\mathbb{F}_p$ for exact Lagrangian Floer homology under a symplectic $\\mathbb{Z}_p$-action, assuming an equivariant stable normal trivialization compatible with the Lagrangians and the required relative Pin data. As an application, we obtain a rank inequality between the symplectic Khovanov homology of a $p$-periodic link and that of its quotient. These results extend the involutive localization of Seidel and Smith. The main construction is a stabilized chain complex. At every invariant intersection point we adjoin the Morse complex of a finite-dimensional normal spectral sphere, whose generators lie in free $\\mathbb{Z}_p$-orbits. The differential counts holomorphic strips coupled to sphere half-trajectories by a one-sided weighted asymptotic evaluation. We prove transversality, a uniform spectral cutoff, and the compactification and gluing statements needed for the chain identity. The stabilized complex is quasi-isomorphic to the ordinary Floer complex and contains the complex of the fixed data as a subcomplex with free quotient, so the algebraic Smith inequality applies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14468",
  "author_total": 3,
  "authors": [
    {
      "name": "Erkao Bao"
    },
    {
      "name": "Tyler Lawson"
    },
    {
      "name": "Cheuk Yu Mak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4w7dtd2hxsqe8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14468",
  "fulltext_url": null,
  "id": "4w7dtd2hxsqe8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14468",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221779680",
  "pdf_url": "https://arxiv.org/pdf/2610.14468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4w7dtd2hxsqe8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.14468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Localization of Lagrangian Floer homology for $\\mathbb{Z}_p$-actions",
  "title_text": "Localization of Lagrangian Floer homology for ℤ_p-actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/4w7dtd2hxsqe8",
  "venue": "arXiv",
  "versions": []
}