{
  "id": "1009.1106",
  "version": "v1",
  "published": "2010-09-06T17:59:28.000Z",
  "updated": "2010-09-06T17:59:28.000Z",
  "title": "On a Generalization of the Flag Complex Conjecture of Charney and Davis",
  "authors": [
    "Kestutis Cesnavicius"
  ],
  "comment": "14 pages, 10 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Flag Complex Conjecture of Charney and Davis states that for a simplicial complex $S$ which triangulates a $(2n - 1)$-generalized homology sphere as a flag complex one has $(-1)^n \\sum_{\\sigma \\in S} \\left(\\frac{-1}{2}\\right)^{\\dim\\sigma + 1} \\ge 0$, where the sum runs over all simplices $\\sigma$ of $S$ (including the empty simplex). Interpreting the $1$-skeleta of $\\sigma\\in S$ as graphs of Coxeter groups, we present a stronger version of this conjecture, and prove the equivalence of the latter to the Flag Complex Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-06T17:59:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "20F55"
    ],
    "keywords": [
      "flag complex conjecture",
      "generalization",
      "davis states",
      "stronger version",
      "coxeter groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1106C"
    }
  }
}