{
  "id": "1407.6767",
  "version": "v3",
  "published": "2014-07-25T00:54:33.000Z",
  "updated": "2016-06-15T13:19:28.000Z",
  "title": "On stacked triangulated manifolds",
  "authors": [
    "Basudeb Datta",
    "Satoshi Murai"
  ],
  "comment": "11 pages, minor changes in the organization of the paper, add information about recent results",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension $d \\geq 4$, if $\\Delta$ is a tight connected closed homology $d$-manifold whose $i$th homology vanishes for $1 < i < d-1$, then $\\Delta$ is a stacked triangulation of a manifold.These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-30T13:26:31.000Z",
      "abstract": "We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) for a connected closed manifold $M$ of dimension $d \\geq 4$, if the $i$th homology group vanishes for $1 <i <d-1$, then any tight triangulation of $M$ is stacked. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.",
      "comment": "11 pages, Corollary 4.4 is added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-06-15T13:19:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "05E45",
      "52B05",
      "57R20",
      "05C40"
    ],
    "keywords": [
      "stacked triangulated manifolds",
      "th homology group vanishes",
      "tight triangulation",
      "combinatorial operations",
      "stacked triangulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.6767D"
    }
  }
}