{
  "id": "1210.1045",
  "version": "v2",
  "published": "2012-10-03T09:27:11.000Z",
  "updated": "2013-06-14T10:41:50.000Z",
  "title": "An infinite family of tight triangulations of manifolds",
  "authors": [
    "Basudeb Datta",
    "Nitin Singh"
  ],
  "comment": "17 pages, Revised, Proof of Lemma 4.1 added, New references added, New Title, Main result is same",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We give an explicit construction of vertex-transitive tight triangulations of $d$-manifolds for $d\\geq 2$. More explicitly, for each $d\\geq 2$, we construct two $(d^2+5d+5)$-vertex neighborly triangulated $d$-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated $d$-manifolds with $2d+3$ vertices constructed by K\\\"{u}hnel. The manifolds we construct are strongly minimal. For $d\\geq 3$, they are also tight neighborly as defined by Lutz, Sulanke and Swartz. Like K\\\"{u}hnel's complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-14T10:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57R05"
    ],
    "keywords": [
      "infinite family",
      "explicit construction",
      "vertex-transitive tight triangulations",
      "odd dimensions",
      "non-trivial series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1045D"
    }
  }
}