{
  "abstract": "We present a new proof of Wolpert's Magic Formula, stating that any Fenchel-Nielsen coordinates on the Teichmüller space of a closed surface are Darboux coordinates for the Weil-Petersson symplectic form. Our approach relies on a de Rham cohomology model for the tangent space to the character variety model of Teichmüller space, in which, by the seminal work of Goldman, the Weil-Petersson form is expressed by a natural symplectic form, called the Goldman form. We extend the work of Fillastre and Seppi, who have managed, using that approach and Stokes's Theorem, to provide a new proof of Wolpert's sum of cosines formula. Using the unique isometric symmetry on any hyperbolic pair of pants, we also introduce a way, given a pair of pants decomposition of a closed surface, to construct an associated linear involution on every tangent space of its Teichmüller space. That allows us to derive a new proof of Wolpert's Magic Formula and deduce a self-contained proof of the closedness of the Goldman form on Teichmüller space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24362",
  "author_total": 1,
  "authors": [
    {
      "name": "Antoine Ablondi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1b0f6vpwqbfpv.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "1b0f6vpwqbfpv",
  "issns": [],
  "landing_url": "https://hal.science/hal-05776703v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ],
    [
      "hal",
      "1.math.math-gt"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05776703/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1b0f6vpwqbfpv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05776703",
      "source": "hal",
      "url": "https://hal.science/hal-05776703v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A De Rham Perspective on the Symplectic Geometry of Teichmüller Space",
  "title_text": "A De Rham Perspective on the Symplectic Geometry of Teichmüller Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:47Z",
  "url": "https://research.draconitic.com/paper/1b0f6vpwqbfpv",
  "venue": "HAL",
  "versions": []
}