{
  "id": "2408.04937",
  "version": "v1",
  "published": "2024-08-09T08:37:29.000Z",
  "updated": "2024-08-09T08:37:29.000Z",
  "title": "A topological proof of Wolpert's formula for the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates",
  "authors": [
    "Nariya Kawazumi"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce a natural cell decomposition of a closed oriented surface associated with a pants decomposition, and an explicit groupoid cocycle on the cell decomposition which represents each point of the Teichm\\\"uller space $\\mathcal{T}_g$. We call it the {\\it standard cocycle} of the point of $\\mathcal{T}_g$. As an application of the explicit description of the standard cocycle, we obtain a topological proof of Wolpert's formula for the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates associated with the pants decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-09T08:37:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weil-petersson symplectic form",
      "wolperts formula",
      "fenchel-nielsen coordinates",
      "topological proof",
      "standard cocycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}