{
  "id": "1509.08221",
  "version": "v1",
  "published": "2015-09-28T07:19:27.000Z",
  "updated": "2015-09-28T07:19:27.000Z",
  "title": "The infinite topology of the hyperelliptic locus in Torelli space",
  "authors": [
    "Kevin Kordek"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.CV",
    "math.GT"
  ],
  "abstract": "Genus $g$ Torelli space is the moduli space of genus $g$ curves of compact type equipped with a homology framing. The hyperelliptic locus is a closed analytic subvariety consisting of finitely many mutually isomorphic components. We use properties of the hyperelliptic Torelli group to show that when $g\\geq 3$ these components do not have the homotopy type of a finite CW complex. Specifically, we show that the second rational homology of each component is infinite-dimensional. We give a more detailed description of the topological features of these components when $g=3$ using properties of genus 3 theta functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-28T07:19:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperelliptic locus",
      "torelli space",
      "infinite topology",
      "second rational homology",
      "finite cw complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150908221K"
    }
  }
}