{
  "id": "1208.0545",
  "version": "v3",
  "published": "2012-08-02T17:11:10.000Z",
  "updated": "2015-01-28T16:16:44.000Z",
  "title": "The simplicial volume of 3-manifolds with boundary",
  "authors": [
    "M. Bucher",
    "R. Frigerio",
    "C. Pagliantini"
  ],
  "comment": "24 pages, 5 figures. Section 6 has been removed, and will appear in a separate paper by the same authors. This version has been accepted for publication by the Journal of Topology",
  "categories": [
    "math.GT",
    "math.AT",
    "math.DG"
  ],
  "abstract": "We provide sharp lower bounds for the simplicial volume of compact $3$-manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of $3$-manifolds, including handlebodies and products of surfaces with the interval. Our results provide the first exact computation of the simplicial volume of a compact manifold whose boundary has positive simplicial volume. We also compute the minimal number of tetrahedra in a (loose) triangulation of the product of a surface with the interval.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-03T17:15:13.000Z",
      "abstract": "We provide sharp lower bounds for the simplicial volume of compact 3-manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of 3-manifolds, including handlebodies and products of surfaces with the interval. Our results provide the first exact computation of the simplicial volume of a compact manifold whose boundary has positive simplicial volume. For the proofs, we use pseudomanifolds to represent integral cycles that approximate the simplicial volume, introduce a topological straightening for aspherical, boundary irreducible manifolds and compute the exact value of the Delta-complexity of products of surfaces with the interval. Finally, we also prove a partial converse of a result by the last two authors regarding the simplicial volume of hyperbolic manifolds with geodesic boundary.",
      "comment": "43 pages; 7 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-28T16:16:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "57N10",
      "57M50",
      "57N65"
    ],
    "keywords": [
      "simplicial volume",
      "represent integral cycles",
      "sharp lower bounds",
      "first exact computation",
      "geodesic boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.0545B"
    }
  }
}