{
  "id": "1104.4796",
  "version": "v3",
  "published": "2011-04-25T20:06:07.000Z",
  "updated": "2011-12-03T21:54:39.000Z",
  "title": "On the homotopy type of the spaces of Morse functions on surfaces",
  "authors": [
    "Elena Kudryavtseva"
  ],
  "comment": "32 pages, in Russian",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let $M$ be a smooth closed orientable surface. Let $F$ be the space of Morse functions on $M$ having fixed number of critical points of each index, moreover at least $\\chi(M)+1$ critical points are labeled by different labels (enumerated). A notion of a skew cylindric-polyhedral complex, which generalizes the notion of a polyhedral complex, is introduced. The skew cylindric-polyhedral complex $\\mathbb{\\widetilde K}$ (the \"complex of framed Morse functions\"), associated with the space $F$, is defined. In the case when $M=S^2$, the polyhedron $\\mathbb{\\widetilde K}$ is finite; its Euler characteristic is evaluated and the Morse inequalities for its Betti numbers are obtained. A relation between the homotopy types of the polyhedron $\\mathbb{\\widetilde K}$ and the space $F$ of Morse functions, endowed with the $C^\\infty$-topology, is indicated.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-03T21:54:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "57M50",
      "58K65",
      "46M18"
    ],
    "keywords": [
      "homotopy type",
      "skew cylindric-polyhedral complex",
      "critical points",
      "smooth closed orientable surface",
      "betti numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4796K"
    }
  }
}