{
  "id": "1204.2693",
  "version": "v3",
  "published": "2012-04-12T11:49:55.000Z",
  "updated": "2015-08-28T09:52:17.000Z",
  "title": "A nice acyclic matching on the nerve of the partition lattice",
  "authors": [
    "Ralf Donau"
  ],
  "comment": "9 pages, 3 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "The author has already proven that the space \\Delta(\\Pi_n)/G is homotopy equivalent to a wedge of spheres of dimension n-3 for all natural numbers n>=3 and all subgroups G<S_1 X S_{n-1}. We wish to construct an acyclic matching on \\Delta(\\Pi_n)/G that allows us to give a basis of its cohomology. This is also a more elementary approach to determining the number of spheres. Furthermore we give a description of the group action by an action on the spheres. We also obtain another result that we call Equivariant Patchwork Theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-16T12:57:01.000Z",
      "comment": "7 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-28T09:52:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nice acyclic matching",
      "partition lattice",
      "equivariant patchwork theorem",
      "homotopy equivalent",
      "group action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2693D"
    }
  }
}