{
  "id": "2004.04219",
  "version": "v1",
  "published": "2020-04-08T19:39:12.000Z",
  "updated": "2020-04-08T19:39:12.000Z",
  "title": "Dehn fillings of knot manifolds containing essential twice-punctured tori",
  "authors": [
    "Steven Boyer",
    "Cameron McA. Gordon",
    "Xingru Zhang"
  ],
  "comment": "103 pages, 46 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that if a hyperbolic knot manifold $M$ contains an essential twice-punctured torus $F$ with boundary slope $\\beta$ and admits a filling with slope $\\alpha$ producing a Seifert fibred space, then the distance between the slopes $\\alpha$ and $\\beta$ is less than or equal to $5$ unless $M$ is the exterior of the figure eight knot. The result is sharp; the bound of $5$ can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the $\\alpha$-filling contains no non-abelian free group. The proofs are divided into the four cases $F$ is a semi-fibre, $F$ is a fibre, $F$ is non-separating but not a fibre, and $F$ is separating but not a semi-fibre, and we obtain refined bounds in each case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-08T19:39:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "essential twice-punctured torus",
      "manifolds containing essential twice-punctured tori",
      "knot manifolds containing essential",
      "dehn fillings",
      "hyperbolic knot manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 103,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}