{
  "id": "math/0506536",
  "version": "v2",
  "published": "2005-06-27T11:16:42.000Z",
  "updated": "2012-05-26T05:34:18.000Z",
  "title": "Combinatorial triangulations of homology spheres",
  "authors": [
    "Bhaskar Bagchi",
    "Basudeb Datta"
  ],
  "comment": "With a correction on Lemma 4.1",
  "journal": "Discrete Mathematics 305 (2005), 1-17",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "Let $M$ be an $n$-vertex combinatorial triangulation of a $\\ZZ_2$-homology $d$-sphere. In this paper we prove that if $n \\leq d + 8$ then $M$ must be a combinatorial sphere. Further, if $n = d + 9$ and $M$ is not a combinatorial sphere then $M$ can not admit any proper bistellar move. Existence of a 12-vertex triangulation of the lens space $L(3, 1)$ shows that the first result is sharp in dimension three. In the course of the proof we also show that any $\\ZZ_2$-acyclic simplicial complex on $\\leq 7$ vertices is necessarily collapsible. This result is best possible since there exist 8-vertex triangulations of the Dunce Hat which are not collapsible.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-26T05:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57R05"
    ],
    "keywords": [
      "homology spheres",
      "combinatorial sphere",
      "vertex combinatorial triangulation",
      "acyclic simplicial complex",
      "proper bistellar move"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6536B"
    }
  }
}