{
  "id": "1212.3303",
  "version": "v2",
  "published": "2012-12-13T20:12:15.000Z",
  "updated": "2014-08-03T20:33:55.000Z",
  "title": "Non-aspherical ends and nonpositive curvature",
  "authors": [
    "Igor Belegradek",
    "T. Tam Nguyen Phan"
  ],
  "comment": "17 pages, editorial changes",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonpositive sectional curvature. If G denotes the fundamental group of B, then a sample result is that B must be aspherical and incompressible if one of the following is true: (1) V has finite volume and G is virtually nilpotent, (2) G is virtually nilpotent and has no proper torsion-free quotients, (3) G is isomorphic to a uniform, irreducible lattice of real rank > 1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-03T20:33:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "nonpositive curvature",
      "non-aspherical ends",
      "complete riemannian metric",
      "virtually nilpotent",
      "proper torsion-free quotients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.3303B"
    }
  }
}