{
  "id": "2304.04392",
  "version": "v1",
  "published": "2023-04-10T05:40:15.000Z",
  "updated": "2023-04-10T05:40:15.000Z",
  "title": "Morse functions with four critical points on immersed 2-spheres",
  "authors": [
    "Svitlana Bilun",
    "Bohdana Hladysh",
    "Alexandr Prishlyak",
    "Mariia Roman"
  ],
  "comment": "9 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We investigate topological properties of simple Morse functions with 4 critical points on immersed 2-spheres. To classify such functions, dual graph of immersion and Reeb graphs is used. We have found all possible structures of the functions:6 structures with 4 critical points on one 1-strata component, 7 structures with two points on the 1-strata and two points on the 2-strata, 7 structures with two 1-stratas and a three-connected 2-strata, three structures with two 1-stratas and without a three-connected 2-strata.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-10T05:40:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "57R70",
      "58C27",
      "G.1.7"
    ],
    "keywords": [
      "critical points",
      "structures",
      "simple morse functions",
      "reeb graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}