{
  "id": "1104.3321",
  "version": "v2",
  "published": "2011-04-17T15:39:40.000Z",
  "updated": "2012-03-23T21:01:11.000Z",
  "title": "Characteristic submanifold theory and toroidal Dehn filling",
  "authors": [
    "Steven Boyer",
    "Cameron McA. Gordon",
    "Xingru Zhang"
  ],
  "comment": "76 pages, 18 figures, minor changes incorporating the referee's comments, to appear in Advances in Mathematics",
  "categories": [
    "math.GT"
  ],
  "abstract": "The exceptional Dehn filling conjecture of the second author concerning the relationship between exceptional slopes $\\alpha, \\beta$ on the boundary of a hyperbolic knot manifold $M$ has been verified in all cases other than small Seifert filling slopes. In this paper we verify it when $\\alpha$ is a small Seifert filling slope and $\\beta$ is a toroidal filling slope in the generic case where $M$ admits no punctured-torus fibre or semi-fibre, and there is no incompressible torus in $M(\\beta)$ which intersects $\\partial M$ in one or two components. Under these hypotheses we show that $\\Delta(\\alpha, \\beta) \\leq 5$. Our proof is based on an analysis of the relationship between the topology of $M$, the combinatorics of the intersection graph of an immersed disk or torus in $M(\\alpha)$, and the two sequences of characteristic subsurfaces associated to an essential punctured torus properly embedded in $M$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-23T21:01:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N10"
    ],
    "keywords": [
      "characteristic submanifold theory",
      "toroidal dehn filling",
      "small seifert filling slope",
      "punctured torus",
      "hyperbolic knot manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 76,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.3321B"
    }
  }
}