{
  "id": "2208.09939",
  "version": "v1",
  "published": "2022-08-21T18:17:54.000Z",
  "updated": "2022-08-21T18:17:54.000Z",
  "title": "The minimal number of critical points of a smooth function on a closed manifold and the ball category",
  "authors": [
    "Rustam Sadykov",
    "Stanislav Trunov"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the minimal number of critical points of a function on a given closed manifold M of dimension at least 6 is the same as the minimal number of elements in a Singhof-Takens filling of M by smooth balls with corners.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-21T18:17:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M30",
      "57R70"
    ],
    "keywords": [
      "minimal number",
      "closed manifold",
      "critical points",
      "ball category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}