{
  "id": "math/9906123",
  "version": "v1",
  "published": "1999-06-18T12:57:37.000Z",
  "updated": "1999-06-18T12:57:37.000Z",
  "title": "Homotopy Groups of the Space of Curves on a Surface",
  "authors": [
    "Vladimir Tchernov"
  ],
  "comment": "8 pages, 1 figure This paper will appear in Math. Scand. probably in Vol. 86, no. 1, 2000",
  "journal": "Math. Scand. 86 (2000), no. 1, 36--44.",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "We explicitly calculate the fundamental group of the space $\\mathcal F$ of all immersed closed curves on a surface $F$. It is shown that $\\pi_n(\\mathcal F)=0$, n>1 for $F\\neq S^2, RP^2$. It is also proved that $\\pi_2(\\mathcal F)=\\Z$, and $\\pi_n(\\mathcal F)=\\pi_n(S^2)\\oplus\\pi_{n+1}(S^2)$, n>2, for $F$ equal to $S^2$ or $RP^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-06-18T12:57:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "57M99"
    ],
    "keywords": [
      "homotopy groups",
      "fundamental group",
      "immersed closed curves"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6123T"
    }
  }
}