{
  "id": "1205.1375",
  "version": "v3",
  "published": "2012-05-07T13:20:07.000Z",
  "updated": "2013-06-26T06:44:43.000Z",
  "title": "Simplicial volume of compact manifolds with amenable boundary",
  "authors": [
    "Sungwoon Kim",
    "Thilo Kuessner"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let $M$ be the interior of a connected, oriented, compact manifold $V$ of dimension at least 2. If each path component of $\\partial V$ has amenable fundamental group, then we prove that the simplicial volume of $M$ is equal to the relative simplicial volume of $V$ and also to the geometric (Lipschitz) simplicial volume of any Riemannian metric on $M$ whenever the latter is finite. As an application we establish the proportionality principle for the simplicial volume of complete, pinched negatively curved manifolds of finite volume.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-26T06:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23"
    ],
    "keywords": [
      "compact manifold",
      "amenable boundary",
      "proportionality principle",
      "riemannian metric",
      "path component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1375K"
    }
  }
}