{
  "id": "0904.0485",
  "version": "v1",
  "published": "2009-04-02T22:57:44.000Z",
  "updated": "2009-04-02T22:57:44.000Z",
  "title": "Heegaard splittings of sufficiently complicated 3-manifolds II: Amalgamation",
  "authors": [
    "David Bachman"
  ],
  "comment": "16 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M_1 and M_2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of \\bdy M_1 to some component of \\bdy M_2 by a homeomorphism \\phi. We show that when \\phi is \"sufficiently complicated\" then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of M_i is an unstabilized splitting of M, (2) every low genus, unstabilized Heegaard splitting of M can be expressed as an amalgamation of unstabilized, boundary-unstabilized splittings of M_i, and possibly a Type II splitting of F \\times I, and (3) if there is no Type II splitting in such an expression then it is unique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-02T22:57:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "amalgamation",
      "low genus",
      "boundary-unstabilized heegaard splittings",
      "homeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0485B"
    }
  }
}