{
  "id": "math/0002002",
  "version": "v1",
  "published": "2000-02-01T02:06:25.000Z",
  "updated": "2000-02-01T02:06:25.000Z",
  "title": "On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds",
  "authors": [
    "Joel Hass",
    "Shicheng Wang",
    "Qing Zhou"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "For any hyperbolic 3-manifold $M$ with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of $\\partial M$ or the volume of $M$ is bounded above. When the volume is bounded above, then area of $\\partial M$ is bounded above and the length of closed geodesic on $\\partial M$ is bounded below.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-01T02:06:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary slopes",
      "finiteness",
      "totally geodesic boundary",
      "uniform bound",
      "essential immersed surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......2002H"
    }
  }
}