{
  "id": "1303.5278",
  "version": "v1",
  "published": "2013-03-21T14:58:31.000Z",
  "updated": "2013-03-21T14:58:31.000Z",
  "title": "1-efficient triangulations and the index of a cusped hyperbolic 3-manifold",
  "authors": [
    "Stavros Garoufalidis",
    "Craig D. Hodgson",
    "J. Hyam Rubinstein",
    "Henry Segerman"
  ],
  "comment": "60 pages, 27 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we will promote the 3D index of an ideal triangulation T of an oriented cusped 3-manifold M (a collection of q-series with integer coefficients, introduced by Dimofte-Gaiotto-Gukov) to a topological invariant of oriented cusped hyperbolic 3-manifolds. To achieve our goal we show that (a) T admits an index structure if and only if T is 1-efficient and (b) if M is hyperbolic, it has a canonical set of 1-efficient ideal triangulations related by 2-3 and 0-2 moves which preserve the 3D index. We illustrate our results with several examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-21T14:58:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M50",
      "57M25"
    ],
    "keywords": [
      "3d index",
      "ideal triangulation",
      "integer coefficients",
      "index structure",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1224834,
      "adsabs": "2013arXiv1303.5278G"
    }
  }
}