{
  "abstract": "For any oriented, smooth $4$--manifold $X$ diffeomorphic to $(S^2\\times S^2)^{\\# n}\\# D^4$, this paper shows that the natural group homomorphism $$\\mathrm{Mod}(X,\\partial X)\\to \\mathrm{O}(H_2(X;\\mathbb{Z}))$$ admits a section. In fact, every light bulb system in $X$ gives rise to a section, which can be characterized uniquely in terms of implanted barbell twists and implanted crossbell involutions. Moreover, all sections arising from different light bulb systems become identical after a single $S^2\\times S^2$--stabilization of $X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27126",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18cg5kvvdc5f4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27126",
  "fulltext_url": null,
  "id": "18cg5kvvdc5f4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27126",
  "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",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223137230",
  "pdf_url": "https://arxiv.org/pdf/2610.27126",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18cg5kvvdc5f4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27126",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27126"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Orthogonal group sections via light bulb systems",
  "title_text": "Orthogonal group sections via light bulb systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/18cg5kvvdc5f4",
  "venue": "arXiv",
  "versions": []
}