{
  "id": "math/0212111",
  "version": "v1",
  "published": "2002-12-08T13:45:58.000Z",
  "updated": "2002-12-08T13:45:58.000Z",
  "title": "Boundary curves of surfaces with the 4-plane property",
  "authors": [
    "Tao Li"
  ],
  "comment": "Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper21.abs.html",
  "journal": "Geom. Topol. 6 (2002) 609-647",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M be an orientable and irreducible 3-manifold whose boundary is an incompressible torus. Suppose that M does not contain any closed nonperipheral embedded incompressible surfaces. We will show in this paper that the immersed surfaces in M with the 4-plane property can realize only finitely many boundary slopes. Moreover, we will show that only finitely many Dehn fillings of M can yield 3-manifolds with nonpositive cubings. This gives the first examples of hyperbolic 3-manifolds that cannot admit any nonpositive cubings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-12-08T13:45:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M25",
      "57N10",
      "57M07"
    ],
    "keywords": [
      "boundary curves",
      "nonpositive cubings",
      "first examples",
      "closed nonperipheral embedded incompressible surfaces",
      "boundary slopes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12111L"
    }
  }
}