{
  "id": "1609.06813",
  "version": "v1",
  "published": "2016-09-22T04:20:39.000Z",
  "updated": "2016-09-22T04:20:39.000Z",
  "title": "Complexity of virtual 3-manifolds",
  "authors": [
    "Evgeny Fominykh",
    "Vladimir Turaev",
    "Andrei Vesnin"
  ],
  "comment": "19 pages",
  "journal": "Sbornik: Mathematics, 207:11 (2016)",
  "categories": [
    "math.GT"
  ],
  "abstract": "Virtual $3$-manifolds were introduced by S.V. Matveev in 2009 as natural generalizations of the classical $3$-manifolds. In this paper, we introduce a notion of complexity of a virtual $3$-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two $2$-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic $3$-manifolds with totally geodesic boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-22T04:20:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M50",
      "57M20"
    ],
    "keywords": [
      "complexity",
      "natural generalizations",
      "special polyhedra",
      "exact values",
      "wide class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}