{
  "id": "1802.08620",
  "version": "v1",
  "published": "2018-02-23T16:12:28.000Z",
  "updated": "2018-02-23T16:12:28.000Z",
  "title": "Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot",
  "authors": [
    "Matthew Hedden",
    "Min Hoon Kim",
    "Thomas E. Mark",
    "Kyungbae Park"
  ],
  "comment": "15 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give infinitely many examples of closed, orientable, irreducible 3-manifolds $M$ such that $b_1(M)=1$ and $\\pi_1(M)$ has weight 1, but $M$ is not the result of Dehn surgery along a knot in the 3-sphere. This answers a question of Aschenbrenner, Friedl and Wilton, and provides the first examples of irreducible manifolds with $b_1=1$ that are known not to be surgery on a knot in the 3-sphere. We further show that our examples are not even homology cobordant to any manifold obtained by Dehn surgery along a knot in the 3-sphere, or any Seifert fibered 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-23T16:12:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dehn surgery",
      "first examples",
      "homology cobordant",
      "irreducible manifolds",
      "aschenbrenner"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}