{
  "id": "1207.6182",
  "version": "v2",
  "published": "2012-07-26T07:04:18.000Z",
  "updated": "2012-08-29T06:49:50.000Z",
  "title": "Tight triangulations of some 4-manifolds",
  "authors": [
    "Basudeb Datta",
    "Nitin Singh"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "Walkup's class ${\\cal K}(d)$ consists of the $d$-dimensional simplicial complexes all whose vertex links are stacked $(d-1)$-spheres. According to a result of Walkup, the face vector of any triangulated 4-manifold $X$ with Euler characteristic $\\chi$ satisfies $f_1 \\geq 5f_0 - 15/2 \\chi$, with equality only for $X \\in {\\cal K}(4)$. K\\\"{u}hnel observed that this implies $f_0(f_0 - 11) \\geq -15\\chi$, with equality only for 2-neighborly members of ${\\cal K}(4)$. For $n = 6, 11$ and 15, there are triangulated 4-manifolds with $f_0=n$ and $f_0(f_0 - 11) = -15\\chi$. In this article, we present triangulated 4-manifolds with $f_0 = 21, 26$ and 41 which satisfy $f_0(f_0 - 11) = -15\\chi$. All these triangulated manifolds are tight and strongly minimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-29T06:49:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57R05"
    ],
    "keywords": [
      "tight triangulations",
      "dimensional simplicial complexes",
      "euler characteristic",
      "face vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.6182D"
    }
  }
}