{
  "abstract": "Under explicit hypotheses on the spectral Looijenga construction, we compute the hyperbolic-plane value of the zero-section invariant of Gukov, Krushkal, Meier, and Pei in periodic topological modular forms. The value is the Hopf element eta, and adjoining a hyperbolic plane acts by multiplication by this element. Earlier work obtains the hyperbolic value under an additional cobordism-duality assumption; here we derive it directly from the Looijenga restriction maps without that assumption. Together with annihilation and vanishing results for definite lattices, this gives a complete value formula on smooth closed simply connected spin four-manifolds. In particular, nonzero signature forces the invariant to vanish, so both orientations of a K3 surface have value zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09819",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuqi Li"
    },
    {
      "name": "Hao-Yu Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enmcj7jz6cyc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09819",
  "fulltext_url": null,
  "id": "enmcj7jz6cyc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09819",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7212150150",
  "pdf_url": "https://arxiv.org/pdf/2609.09819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enmcj7jz6cyc8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The hyperbolic class and vanishing laws in a TMF-valued four-manifold invariant",
  "title_text": "The hyperbolic class and vanishing laws in a TMF-valued four-manifold invariant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/enmcj7jz6cyc8",
  "venue": "arXiv",
  "versions": []
}