{
  "id": "2212.05769",
  "version": "v1",
  "published": "2022-12-12T08:43:06.000Z",
  "updated": "2022-12-12T08:43:06.000Z",
  "title": "A standard form of incompressible surfaces in 3-dimensional handlebodies",
  "authors": [
    "Wei Lin",
    "Fengchun Lei"
  ],
  "comment": "19 pages, 13 figures. Accepted for publication in SCIENCE CHINA Mathematics",
  "categories": [
    "math.GT"
  ],
  "abstract": "Applying Morse theory, we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional handlebodies. We also give a necessary and sufficient condition to determine the incompressibility of such surfaces placed in our standard form. Our algorithm is practical. Several examples are given to test the algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-12T08:43:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K30",
      "57N75",
      "57R65"
    ],
    "keywords": [
      "standard form",
      "handlebodies",
      "applying morse theory",
      "sufficient condition",
      "properly embedded incompressible surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}