{
  "id": "1709.03804",
  "version": "v1",
  "published": "2017-09-12T12:26:02.000Z",
  "updated": "2017-09-12T12:26:02.000Z",
  "title": "Elimination of definite fold II",
  "authors": [
    "Osamu Saeki"
  ],
  "comment": "9 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we first give a detailed proof to the elimination theorem of definite folds for smooth maps of manifolds of dimension > 2 into the 2-sphere or into the real projective plane, as the proof given in our previous paper lacked some detailed explanations. We also give a new proof from a different viewpoint and also present various explicit examples. Furthermore, we prove the non-existence of singular Legendre fibrations on 3-manifolds, answering negatively to a question posed in our previous paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-12T12:26:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "57R35",
      "58K30"
    ],
    "keywords": [
      "definite fold",
      "singular legendre fibrations",
      "elimination theorem",
      "explicit examples",
      "smooth maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}