{
  "id": "1801.01858",
  "version": "v1",
  "published": "2018-01-05T18:08:44.000Z",
  "updated": "2018-01-05T18:08:44.000Z",
  "title": "Special moves for open book decompositions of 3-manifolds",
  "authors": [
    "Riccardo Piergallini",
    "Daniele Zuddas"
  ],
  "comment": "16 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-05T18:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N12",
      "55R55",
      "57R17"
    ],
    "keywords": [
      "open book decompositions",
      "special moves",
      "special local version",
      "book decompositions representing homologous contact",
      "decompositions representing homologous contact structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}