{
  "id": "1209.5819",
  "version": "v2",
  "published": "2012-09-26T02:33:22.000Z",
  "updated": "2012-11-16T16:27:45.000Z",
  "title": "Fenchel-Nielsen coordinates on upper bounded pants decompositions",
  "authors": [
    "Dragomir Šarić"
  ],
  "comment": "proof in Step III, Theorem 2.1 simplified, statements unchanged",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Let $X_0$ be an infinite genus hyperbolic surface (whose boundary components, if any, are closed geodesics or punctures) which has an upper bounded pants decomposition. The length spectrum Teichm\\\"uller space $T_{ls}(X_0)$ consists of all surfaces $X$ homeomorphic to $X_0$ such that the ratios of the corresponding simple closed geodesics are uniformly bounded from below and from above. Alessandrini, Liu, Papadopoulos and Su described the Fenchel-Nielsen coordinates for $T_{ls}(X_0)$ and using these coordinates they proved that $T_{ls}(X_0)$ is path connected. We use the Fenchel-Nielsen coordinates for $T_{ls}(X_0)$ to induce a locally biLipschitz homeomorphism between $l^{\\infty}$ and $T_{ls}(X_0)$ (which extends analogous results by Fletcher and by Allessandrini, Liu, Papadopoulos, Su and Sun for the unreduced and the reduced $T_{qc}(X_0)$). Consequently, $T_{ls}(X_0)$ is contractible. We also characterize the closure in the length spectrum metric of the quasiconformal Teichm\\\"uller space $T_{qc}(X_0)$ in $T_{ls}(X_0)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-16T16:27:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15"
    ],
    "keywords": [
      "upper bounded pants decomposition",
      "fenchel-nielsen coordinates",
      "infinite genus hyperbolic surface",
      "closed geodesics",
      "length spectrum metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5819S"
    }
  }
}