{
  "id": "math/0608635",
  "version": "v4",
  "published": "2006-08-25T16:28:29.000Z",
  "updated": "2012-04-21T19:16:23.000Z",
  "title": "Heegaard splittings and 1-relator groups",
  "authors": [
    "Joseph D. Masters"
  ],
  "comment": "Paper has been withdrawn by the author due to a gap in the proof of main theorem",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that if $M$ is a fibered, orientable 3-manifold, and if $\\pi_1 M$ has 1-relator presentation, then the presentation is induced by a Heegaard splitting of $M$. A corollary is that, for these manifolds, the rank of $\\pi_1 M$ is equal to the \"restricted\" Heegaard genus of $M$. We also explore the analogy between 1-relator groups and Haken 3-manifolds, showing that every 1-relator group possesses a \"1-relator hierarchy\".",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-04-21T19:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "57M07"
    ],
    "keywords": [
      "heegaard splitting",
      "group possesses",
      "heegaard genus",
      "presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}