{
  "id": "2411.04463",
  "version": "v1",
  "published": "2024-11-07T06:24:10.000Z",
  "updated": "2024-11-07T06:24:10.000Z",
  "title": "Morse inequalities for noncompact manifolds",
  "authors": [
    "Tsuyoshi Kato",
    "Daisuke Kishimoto",
    "Mitsunobu Tsutaya"
  ],
  "comment": "28 pages",
  "categories": [
    "math.GT",
    "math.AT",
    "math.DG"
  ],
  "abstract": "We establish Morse inequalities for a noncompact manifold with a cocompact and properly discontinuous action of a discrete group, where Morse functions are not necessarily invariant under the group action. The inequalities are given in terms of the $L^2$-Betti numbers and functions on the acting group which describe rough configurations of critical points of a Morse function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-07T06:24:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R19",
      "58E05"
    ],
    "keywords": [
      "noncompact manifold",
      "morse function",
      "discrete group",
      "establish morse inequalities",
      "group action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}