{
  "id": "1908.03014",
  "version": "v1",
  "published": "2019-08-08T10:59:58.000Z",
  "updated": "2019-08-08T10:59:58.000Z",
  "title": "First Betti numbers of orbits of Morse functions on surfaces",
  "authors": [
    "Iryna Kuznietsova",
    "Yuliia Soroka"
  ],
  "categories": [
    "math.GR",
    "math.AT",
    "math.GT",
    "math.KT"
  ],
  "abstract": "In this article we study algebraic properties of the specific class of groups $\\mathcal{G}$ generated by direct products and wreath products. Such class of groups appears in calculation of fundamental groups of orbits of Morse functions on compact manifolds. We prove that for any group $G\\in\\mathcal{G}$ the ranks of the center $Z(G)$ and the quotient by commutator subgroup $G/[G,G]$ coincide. Moreover, this rank is a first Betti number of the orbit of Morse function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-08T10:59:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E22",
      "20F16",
      "57T15"
    ],
    "keywords": [
      "first betti number",
      "morse function",
      "study algebraic properties",
      "compact manifolds",
      "direct products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}