{
  "abstract": "We show that for an arbitrary compact orientable smooth $4$--dimensional manifold $M$ with a given open book structure on the boundary $\\partial M \\neq \\emptyset$, which may be disconnected, there exists a generic smooth map of $M$ onto the $2$--disk which gives a relative trisection on $M$ consistent with the given open book structure on $\\partial M$. This gives a new proof to the existence of a relative trisection on $M$. In fact, it turns out that every relative trisection can be obtained in this way. As a byproduct, we also show that $M$ always admits a decomposition into a PALF (positive allowable Lefschetz fibration) over the $2$--disk $D^2$ and a fiber bundle over the circle with a sutured compression body fiber, consistent with the given open book structure on $\\partial M$ and with the surface bundle structure of the PALF over $\\partial D^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02494",
  "author_total": 1,
  "authors": [
    {
      "name": "Osamu Saeki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nhvrjkj08ay2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02494",
  "fulltext_url": null,
  "id": "5nhvrjkj08ay2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02494",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5nhvrjkj08ay2.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Relative trisection maps on 4-manifolds",
  "title_text": "Relative trisection maps on 4-manifolds",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/5nhvrjkj08ay2",
  "venue": "arXiv",
  "versions": []
}