{
  "abstract": "The existence of a transverse metric on a foliated manifold is typically used as a framework for studying transversely elliptic basic differential operators. This article details a method for constructing such a transverse metric directly from the principal symbol of the operator. Consequently, rather than treating the transverse metric as a mere working assumption, we demonstrate that its existence is a necessary condition for the very presence of a transversely elliptic operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07903",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenran Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdxpvv3527zae.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07903",
  "fulltext_url": null,
  "id": "cdxpvv3527zae",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07903",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdxpvv3527zae.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds",
  "title_text": "Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/cdxpvv3527zae",
  "venue": "arXiv",
  "versions": []
}