{
  "abstract": "We prove that there exist hyperbolic integer homology spheres with arbitrarily large Dehn surgery number. Previously, no integer homology sphere was known to have a surgery number larger than $2$. Our approach uses Froyshov's invariant $q_3$ of integer homology spheres, which is defined in terms of mod 2 instanton homology. We show that if $W: Y \\to Y'$ is a cobordism between integer homology spheres with no $2$-torsion in its first homology, then $-b^+(W) \\le q_3(Y') - q_3(Y) \\le b^-(W)$. We also extend both $q_3$ and the inequality to rational homology spheres.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27904",
  "author_total": 3,
  "authors": [
    {
      "name": "Aliakbar Daemi"
    },
    {
      "name": "Xingpei Liu"
    },
    {
      "name": "Mike Miller Eismeier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kz2q4j7rcaan.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27904",
  "fulltext_url": null,
  "id": "6kz2q4j7rcaan",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27904",
  "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"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204807406",
  "pdf_url": "https://arxiv.org/pdf/2608.27904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kz2q4j7rcaan.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Instantons, indefinite 4-manifolds, and Dehn surgery",
  "title_text": "Instantons, indefinite 4-manifolds, and Dehn surgery",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/6kz2q4j7rcaan",
  "venue": "arXiv",
  "versions": []
}