{
  "id": "1104.4792",
  "version": "v2",
  "published": "2011-04-25T20:02:49.000Z",
  "updated": "2011-06-15T22:27:21.000Z",
  "title": "Topology of the spaces of Morse functions on surfaces",
  "authors": [
    "Elena Kudryavtseva"
  ],
  "comment": "15 pages, in Russian",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let $M$ be a smooth closed orientable surface, and let $F$ be the space of Morse functions on $M$ such that at least $\\chi(M)+1$ critical points of each function of $F$ are labeled by different labels (enumerated). Endow the space $F$ with $C^\\infty$-topology. We prove the homotopy equivalence $F\\sim R\\times{\\widetilde{\\cal M}}$ where $R$ is one of the manifolds ${\\mathbb R}P^3$, $S^1\\times S^1$ and the point in dependence on the sign of $\\chi(M)$, and ${\\widetilde{\\cal M}}$ is the universal moduli space of framed Morse functions, which is a smooth stratified manifold. Morse inequalities for the Betti numbers of the space $F$ are obtained.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-15T22:27:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "57M50",
      "58K65",
      "46M18"
    ],
    "keywords": [
      "universal moduli space",
      "smooth closed orientable surface",
      "homotopy equivalence",
      "framed morse functions",
      "smooth stratified manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4792K"
    }
  }
}