{
  "id": "1406.6067",
  "version": "v2",
  "published": "2014-06-23T20:00:48.000Z",
  "updated": "2014-07-29T17:05:37.000Z",
  "title": "Order complexes of coset posets of finite groups are not contractible",
  "authors": [
    "John Shareshian",
    "Russ Woodroofe"
  ],
  "comment": "16 pages. v2 fixes minor errors",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We show that the order complex of the poset of all cosets of all proper subgroups of a finite group $G$ is never $\\mathbb{F}_{2}$-acyclic and therefore never contractible. This settles a question of K. S. Brown.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-29T17:05:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "20E99",
      "06B30"
    ],
    "keywords": [
      "finite group",
      "coset posets",
      "order complexes",
      "contractible"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.6067S"
    }
  }
}