{
  "id": "1001.4259",
  "version": "v2",
  "published": "2010-01-24T17:30:00.000Z",
  "updated": "2013-02-27T20:03:17.000Z",
  "title": "Surfaces that become isotopic after Dehn filling",
  "authors": [
    "David Bachman",
    "Ryan Derby-Talbot",
    "Eric Sedgwick"
  ],
  "comment": "Revised version, incorporates updated references and improved exposition",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that after generic filling along a torus boundary component of a 3-manifold, no two closed, 2-sided, essential surfaces become isotopic, and no closed, 2-sided, essential surface becomes inessential. That is, the set of essential surfaces (considered up to isotopy) survives unchanged in all suitably generic Dehn fillings. Furthermore, for all but finitely many non-generic fillings, we show that two essential surfaces can only become isotopic in a constrained way.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-27T20:03:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "essential surface",
      "torus boundary component",
      "suitably generic dehn fillings",
      "non-generic fillings",
      "inessential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.4259B"
    }
  }
}