{
  "id": "math/0702680",
  "version": "v1",
  "published": "2007-02-23T05:46:54.000Z",
  "updated": "2007-02-23T05:46:54.000Z",
  "title": "Diameters of 3-Sphere Quotients",
  "authors": [
    "W. Dunbar",
    "S. Greenwald",
    "J. McGowan",
    "C. Searle"
  ],
  "comment": "The figure on page 12 previews and prints reliably with Adobe Reader",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let G, a subset of O(4), act isometrically on the 3-sphere. In this article we calculate a lower bound for the diameter of the quotient spaces $S^3/G$. We find it to be ${1/2}\\arccos(\\frac{\\tan(\\frac{3 \\pi}{10})}{\\sqrt3})$, which is exactly the value of the lower bound for diameters of the spherical space forms. In the process, we are also able to find a lower bound for diameters for the spherical Aleksandrov spaces, $S^n/G$, of cohomogeneities 1 and 2, as well as for cohomogeneity 3 (with some restrictions on the group type). This leads us to conjecture that the diameter of $S^n/G$ is increasing as the cohomogeneity of the group $G$ increases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-23T05:46:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "lower bound",
      "cohomogeneity",
      "spherical space forms",
      "quotient spaces",
      "spherical aleksandrov spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2680D"
    }
  }
}