{
  "id": "1601.02283",
  "version": "v1",
  "published": "2016-01-11T00:00:10.000Z",
  "updated": "2016-01-11T00:00:10.000Z",
  "title": "Topology of the spaces of functions with prescribed singularities on surfaces",
  "authors": [
    "Elena A. Kudryavtseva"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M$ be a smooth connected orientable closed surface and $f_0\\in C^\\infty(M)$ a function having only critical points of the $A_\\mu$-types, $\\mu\\in\\mathbb N$. Let ${\\mathcal F}={\\mathcal F}(f_0)$ be the set of functions $f\\in C^\\infty(M)$ having the same types of local singularities as those of $f_0$. We describe the homotopy type of the space $\\mathcal F$, endowed with the $C^\\infty$-topology, and its decomposition into orbits of the action of the group of \"left-right changings of coordinates\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-11T00:00:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "57M50",
      "58K65",
      "46M18"
    ],
    "keywords": [
      "prescribed singularities",
      "local singularities",
      "homotopy type",
      "smooth connected orientable closed surface",
      "left-right changings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102283K"
    }
  }
}