{
  "id": "1106.3116",
  "version": "v1",
  "published": "2011-06-15T22:53:18.000Z",
  "updated": "2011-06-15T22:53:18.000Z",
  "title": "Special framed Morse functions on surfaces",
  "authors": [
    "Elena A. Kudryavtseva"
  ],
  "comment": "8 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 $M$, and $\\mathbb{F}^1$ the space of framed Morse functions, both endowed with $C^\\infty$-topology. The space $\\mathbb{F}^0$ of special framed Morse functions is defined. We prove that the inclusion mapping $\\mathbb{F}^0\\hookrightarrow\\mathbb{F}^1$ is a homotopy equivalence. In the case when at least $\\chi(M)+1$ critical points of each function of $F$ are labeled, homotopy equivalences $\\mathbb{\\widetilde K}\\sim\\widetilde{\\cal M}$ and $F\\sim\\mathbb{F}^0\\sim{\\mathscr D}^0\\times\\mathbb{\\widetilde K}$ are proved, where $\\mathbb{\\widetilde K}$ is the complex of framed Morse functions, $\\widetilde{\\cal M}\\approx\\mathbb{F}^1/{\\mathscr D}^0$ is the universal moduli space of framed Morse functions, ${\\mathscr D}^0$ is the group of self-diffeomorphisms of $M$ homotopic to the identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-15T22:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "57M50",
      "58K65",
      "46M18"
    ],
    "keywords": [
      "special framed morse functions",
      "homotopy equivalence",
      "universal moduli space",
      "smooth closed orientable surface",
      "critical points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3116K"
    }
  }
}