{
  "id": "1410.8590",
  "version": "v1",
  "published": "2014-10-30T23:55:02.000Z",
  "updated": "2014-10-30T23:55:02.000Z",
  "title": "Homotopy type of spaces of curves with constrained curvature on flat surfaces",
  "authors": [
    "Nicolau C. Saldanha",
    "Pedro Zühlke"
  ],
  "comment": "38 pages, 13 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Let $S$ be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on $S$ which start and end at given points in given directions and whose curvatures are constrained to lie in a given open interval, in terms of all parameters involved. Any connected component of such a space is either contractible or homotopy equivalent to an $n$-sphere, and every $n\\geq 1$ is realizable. Explicit homotopy equivalences between the components and the corresponding spheres are constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-30T23:55:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D10",
      "53C42"
    ],
    "keywords": [
      "homotopy type",
      "constrained curvature",
      "explicit homotopy equivalences",
      "complete flat surface",
      "open interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.8590S"
    }
  }
}