{
  "id": "1107.3433",
  "version": "v2",
  "published": "2011-07-18T13:34:36.000Z",
  "updated": "2011-10-27T08:13:16.000Z",
  "title": "A Lower Bound for the Number of Group Actions on a Compact Riemann Surface",
  "authors": [
    "James W. Anderson",
    "Aaron Wootton"
  ],
  "journal": "Algebr. Geom. Topol. 12 (2012), 19--35",
  "doi": "10.2140/agt.2012.12.19",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\\sigma \\geq 2$ is at least quadratic in $\\sigma$. We do this through the introduction of a coarse signature space, the space $\\mathcal{K}_\\sigma$ of {\\em skeletal signatures} of group actions on compact Riemann surfaces of genus $\\sigma$. We discuss the basic properties of $\\mathcal{K}_\\sigma$ and present a full conjectural description.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-27T08:13:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "30F20",
      "14H37"
    ],
    "keywords": [
      "compact riemann surface",
      "lower bound",
      "distinct group actions",
      "coarse signature space",
      "full conjectural description"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.3433A"
    }
  }
}