{
  "id": "1411.6349",
  "version": "v1",
  "published": "2014-11-24T05:13:28.000Z",
  "updated": "2014-11-24T05:13:28.000Z",
  "title": "Optimal sweepouts of a Riemannian 2-sphere",
  "authors": [
    "Gregory R. Chambers",
    "Yevgeny Liokumovich"
  ],
  "comment": "21 pages, 9 figures",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We prove the following conjecture of R. Rotman. Suppose we are given an epsilon > 0 and a sweepout of a Riemannian 2-sphere which is composed of curves of length at most L. We can then find a second sweepout which is composed of curves of length at most L + epsilon, which are pairwise disjoint, and which are either constant curves or simple curves. We use the techniques involved in proving this statement to partly answer a question due to N. Hingston and H.-B. Rachemacher, and we also use these methods to extend the results of [CL] concerning converting homotopies to isotopies in an effective way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-24T05:13:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23"
    ],
    "keywords": [
      "optimal sweepouts",
      "riemannian",
      "second sweepout",
      "simple curves",
      "constant curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6349C"
    }
  }
}