{
  "id": "math/0608137",
  "version": "v4",
  "published": "2006-08-05T09:34:46.000Z",
  "updated": "2009-03-31T20:05:32.000Z",
  "title": "Heegaard splittings of knot exteriors",
  "authors": [
    "Yoav Moriah"
  ],
  "comment": "This is the version published by Geometry & Topology Monographs on 3 December 2007",
  "journal": "Geom. Topol. Monogr. 12 (2007) 191-232",
  "doi": "10.2140/gtm.2007.12.191",
  "categories": [
    "math.GT"
  ],
  "abstract": "The goal of this paper is to offer a comprehensive exposition of the current knowledge about Heegaard splittings of exteriors of knots in the 3-sphere. The exposition is done with a historical perspective as to how ideas developed and by whom. Several new notions are introduced and some facts about them are proved. In particular the concept of a 1/n-primitive meridian. It is then proved that if a knot K in S^3 has a 1/n-primitive meridian; then nK = K#...#K, n-times has a Heegaard splitting of genus nt(K) + n which has a 1-primitive meridian. That is, nK is mu-primitive.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-03-31T20:05:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M05"
    ],
    "keywords": [
      "heegaard splitting",
      "knot exteriors",
      "current knowledge",
      "genus nt",
      "comprehensive exposition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8137M"
    }
  }
}