{
  "id": "math/0509679",
  "version": "v1",
  "published": "2005-09-28T23:30:25.000Z",
  "updated": "2005-09-28T23:30:25.000Z",
  "title": "A Uniqueness Property for the Quantization of Teichmüller Spaces",
  "authors": [
    "Hua Bai"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "Chekhov, Fock and Kashaev introduced a quantization of the Teichm\\\"{u}ller space $\\mathcal{T}^q(S)$ of a punctured surface $S$, and an exponential version of this construction was developed by Bonahon and Liu. The construction of the quantum Teichm\\\"{u}ller space crucially depends on certain coordinate change isomorphisms between the Chekhov-Fock algebras associated to different ideal triangulations of $S$. We show that these coordinate change isomorphisms are essentially unique, once we require them to satisfy a certain number of natural conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-28T23:30:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57R56",
      "20G42"
    ],
    "keywords": [
      "teichmüller spaces",
      "uniqueness property",
      "coordinate change isomorphisms",
      "quantization",
      "natural conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9679B"
    }
  }
}