{
  "id": "0810.0174",
  "version": "v1",
  "published": "2008-10-01T14:33:26.000Z",
  "updated": "2008-10-01T14:33:26.000Z",
  "title": "Euler characteristic and quadrilaterals of normal surfaces",
  "authors": [
    "Tejas Kalelkar"
  ],
  "comment": "7 pages, 1 figure",
  "journal": "Proceedings Mathematical Sciences, Indian Academy of Sciences, Volume 118, Number 2 / May, 2008, Pg 227-233",
  "doi": "10.1007/s12044-008-0015-7",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M$ be a compact 3-manifold with a triangulation $\\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial description. Secondly, we obtain an inequality relating the number of normal triangles and normal quadrilaterals of $F$, that depends on the maximum number of tetrahedrons that share a vertex in $\\tau$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-01T14:33:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q35",
      "57M99"
    ],
    "keywords": [
      "euler characteristic",
      "normal surfaces",
      "normal quadrilaterals",
      "inequality relating",
      "combinatorial description"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0174K"
    }
  }
}