{
  "id": "1709.03328",
  "version": "v1",
  "published": "2017-09-11T10:58:23.000Z",
  "updated": "2017-09-11T10:58:23.000Z",
  "title": "Extending a Morse function to a non-orientable $3-$manifold",
  "authors": [
    "Clément Laroche"
  ],
  "comment": "Master thesis supervised by Thomas Fiedler",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "Considering a solid 3-dimensional Klein bottle and a collaring of its boundary, can we extend a generic $C^\\infty$ non-singular function defined on the collaring to the full solid Klein bottle without critical points? We give a condition on the Reeb graph of the given function that is necessary and sufficient for the existence of such a non-singular extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-11T10:58:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "58E05"
    ],
    "keywords": [
      "morse function",
      "full solid klein bottle",
      "non-singular extension",
      "reeb graph",
      "non-singular function"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}