{
  "id": "1208.1663",
  "version": "v2",
  "published": "2012-08-08T13:44:24.000Z",
  "updated": "2015-10-07T13:27:52.000Z",
  "title": "The 3D index of an ideal triangulation and angle structures",
  "authors": [
    "Stavros Garoufalidis"
  ],
  "comment": "28 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The 3D index of Dimofte-Gaiotto-Gukov a partially defined function on the set of ideal triangulations of 3-manifolds with $r$ torii boundary components. For a fixed $2r$ tuple of integers, the index takes values in the set of $q$-series with integer coefficients. Our goal is to give an axiomatic definition of the tetrahedron index, and a proof that the domain of the 3D index consists precisely of the set of ideal triangulations that support an index structure. The latter is a generalization of a strict angle structure. We also prove that the 3D index is invariant under 3-2 moves, but not in general under 2-3 moves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-08T13:44:24.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-10-07T13:27:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ideal triangulation",
      "strict angle structure",
      "torii boundary components",
      "index structure",
      "axiomatic definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1663G"
    }
  }
}