{
  "id": "1305.1597",
  "version": "v1",
  "published": "2013-05-07T18:10:10.000Z",
  "updated": "2013-05-07T18:10:10.000Z",
  "title": "Exceptional surgeries on knots with exceptional classes",
  "authors": [
    "Scott A. Taylor"
  ],
  "comment": "This paper is written in the style of a survey article. Comments are welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot $\\beta$ in a compact, orientable, hyperbolic 3-manifold $M$ has the property that winding number and wrapping number are not equal with respect to a non-trivial class in $H_2(M,\\boundary M)$, then, with only a few possible exceptions, every 3-manifold $M'$ obtained by Dehn surgery on $\\beta$ with surgery distance $\\Delta \\geq 2$ will be hyperbolic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-07T18:10:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional surgeries",
      "exceptional classes",
      "study exceptional dehn fillings",
      "hyperbolic",
      "classical combinatorial sutured manifold theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.1597T"
    }
  }
}