{
  "id": "1005.0329",
  "version": "v2",
  "published": "2010-05-03T15:55:37.000Z",
  "updated": "2011-03-17T12:17:40.000Z",
  "title": "Generalized Mom-structures and ideal triangulations of 3-manifolds with non-spherical boundary",
  "authors": [
    "Ekaterina Pervova"
  ],
  "comment": "38 pages, 19 figues; exposition style changed, particularly in Section 2.2; minor content changes in Section 2.1",
  "categories": [
    "math.GT"
  ],
  "abstract": "The so-called Mom-structures on hyperbolic cusped 3-manifolds without boundary were introduced by Gabai, Meyerhoff, and Milley, and used by them to identify the smallest closed hyperbolic manifold. In this work we extend the notion of a Mom-structure to include the case of 3-manifolds with non-empty boundary that does not have spherical components. We then describe a certain relation between such generalized Mom-structures, called protoMom-structures, internal on a fixed 3-manifold N, and ideal triangulations of N; in addition, in the case of non-closed hyperbolic manifolds without annular cusps, we describe how an internal geometric protoMom-structure can be constructed starting from Epstein-Penner or Kojima decomposition. Finally, we exhibit a set of combinatorial moves that relate any two internal protoMom-structures on a fixed N to each other.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-17T12:17:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M20",
      "57N10",
      "57M15",
      "57M50"
    ],
    "keywords": [
      "ideal triangulations",
      "generalized mom-structures",
      "non-spherical boundary",
      "smallest closed hyperbolic manifold",
      "internal geometric protomom-structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.0329P"
    }
  }
}