{
  "id": "1601.00065",
  "version": "v1",
  "published": "2016-01-01T09:28:49.000Z",
  "updated": "2016-01-01T09:28:49.000Z",
  "title": "A characterization of tightly triangulated 3-manifolds",
  "authors": [
    "Bhaskar Bagchi",
    "Basudeb Datta",
    "Jonathan Spreer"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "For a field $\\mathbb{F}$, the notion of $\\mathbb{F}$-tightness of simplicial complexes was introduced by K\\\"uhnel. K\\\"uhnel and Lutz conjectured that any $\\mathbb{F}$-tight triangulation of a closed manifold is the most economic of all possible triangulations of the manifold. The boundary of a triangle is the only $\\mathbb{F}$-tight triangulation of a closed 1-manifold. A triangulation of a closed 2-manifold is $\\mathbb{F}$-tight if and only if it is $\\mathbb{F}$-orientable and neighbourly. In this paper we prove that a triangulation of a closed 3-manifold is $\\mathbb{F}$-tight if and only if it is $\\mathbb{F}$-orientable, neighbourly and stacked. In consequence, the K\\\"uhnel-Lutz conjecture is valid in dimension $\\leq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-01T09:28:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57R05"
    ],
    "keywords": [
      "characterization",
      "tight triangulation",
      "simplicial complexes",
      "closed manifold",
      "consequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160100065B"
    }
  }
}