{
  "abstract": "In this paper, building on the work of Dai--Sasahira--Stoffregen, we derive constraints on the intersection forms of smooth, compact, indefinite, spin $4$-manifolds bounded by AR homology spheres using two methods. First, we use the constraints on the existence of $\\operatorname{Pin}(2)$-equivariant maps between representation spheres, established by Hopkins--Lin--Shi--Xu in their proof of the $10/8 + 4$-inequality. Second, we compute Lin's $κo$-invariant for AR homology spheres. Combined with Lin's version of the relative $10/8$-inequality, this computation yields constraints different from those based on Hopkins--Lin--Shi--Xu. As applications, we obtain new lower bounds on the minimal genus of surfaces bounded by knots whose double branched covers are AR homology spheres in various $4$-manifolds, and provide an obstruction to smooth $4$-manifold decompositions related to the $11/8$-conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35931",
  "author_total": 1,
  "authors": [
    {
      "name": "Eiichiro Hakamada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bsx9bnc5bw7g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35931",
  "fulltext_url": null,
  "id": "2bsx9bnc5bw7g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35931",
  "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": "W7214977948",
  "pdf_url": "https://arxiv.org/pdf/2609.35931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bsx9bnc5bw7g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On intersection forms of spin $4$-manifolds with AR homology sphere boundary",
  "title_text": "On intersection forms of spin $4$-manifolds with AR homology sphere boundary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/2bsx9bnc5bw7g",
  "venue": "arXiv",
  "versions": []
}