{
  "abstract": "We study the geography of taut foliations on compact $3$-manifolds with toroidal boundary components. The central object of our work is the set of boundary multislopes realized by foliations transverse to a fixed flow on such a manifold. We prove that these sets exhibit remarkable structural properties (rationality, rigidity, and convexity) which motivate the name ziggurats. Our main tool, of independent interest, is a two-way correspondence between foliations and contact structures on $3$-manifolds with boundary: we generalize the Eliashberg-Thurston theorem, which produces pairs of positive and negative contact structures from foliations, and a construction of the first author, which builds foliations from such contact pairs. Using both directions of this correspondence, we bring contact-geometric methods to bear on the architecture of ziggurats.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30031",
  "author_total": 2,
  "authors": [
    {
      "name": "Thomas Massoni"
    },
    {
      "name": "Jonathan Zung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jgm4zyeee36m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30031",
  "fulltext_url": null,
  "id": "1jgm4zyeee36m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30031",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
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  ],
  "openalex": "W7204893824",
  "pdf_url": "https://arxiv.org/pdf/2608.30031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jgm4zyeee36m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2608.30031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ziggurats, taut foliations, and contact structures",
  "title_text": "Ziggurats, taut foliations, and contact structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1jgm4zyeee36m",
  "venue": "arXiv",
  "versions": []
}