{
  "id": "1810.01563",
  "version": "v1",
  "published": "2018-10-03T02:04:07.000Z",
  "updated": "2018-10-03T02:04:07.000Z",
  "title": "The realization problem for non-integer Seifert fibered surgeries",
  "authors": [
    "Ahmad Issa",
    "Duncan McCoy"
  ],
  "comment": "30 pages, 15 figures. Comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "Conjecturally, the only knots in $S^3$ with non-integer surgeries producing Seifert fibered spaces are torus knots and cables of torus knots. In this paper, we make progress on the associated realization problem. Let $Y$ be a small Seifert fibered space bounding a positive definite plumbing with central vertex of weight $e$ such that $Y$ arises by non-integer $p/q$-surgery on a knot in $S^3$. We show that if $e\\geq 2$ and the slope $p/q$ is negative, or $e\\geq 3$ and $p/q$ is positive, then $Y$ can be obtained by $p/q$-surgery on a torus knot or a cable of a torus knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-03T02:04:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-integer seifert fibered surgeries",
      "realization problem",
      "torus knot",
      "seifert fibered space bounding",
      "surgeries producing seifert fibered spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}