{
  "id": "1606.05459",
  "version": "v1",
  "published": "2016-06-17T09:25:00.000Z",
  "updated": "2016-06-17T09:25:00.000Z",
  "title": "Plant complexes and homological stability for Hurwitz spaces",
  "authors": [
    "J. Frederik Tietz"
  ],
  "comment": "34 pages, 21 figures, comments welcome!",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We study Hurwitz spaces with regard to homological stabilization. By a Hurwitz space, we mean a moduli space of branched, not necessarily connected coverings of a disk with fixed structure group and number of branch points. We choose a sequence of subspaces of Hurwitz spaces which is suitable for our investigations. In the first part, we introduce and study plant complexes, a large new class of simplicial complexes, generalizing the arc complex on a surface with marked points. In the second part, we generalize a result by Ellenberg-Venkatesh-Westerland by showing that homological stabilization of our sequence of Hurwitz spaces depends only on properties of their zeroth homology groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-17T09:25:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M12",
      "14H15",
      "55R80",
      "05E45",
      "20F36"
    ],
    "keywords": [
      "homological stability",
      "homological stabilization",
      "study hurwitz spaces",
      "study plant complexes",
      "zeroth homology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}