{
  "id": "math/9904096",
  "version": "v1",
  "published": "1999-04-19T17:12:06.000Z",
  "updated": "1999-04-19T17:12:06.000Z",
  "title": "On Loops Representing Elements of the Fundamental Group of a Complete Manifold with Nonnegative Ricci Curvature",
  "authors": [
    "Christina Sormani"
  ],
  "comment": "19 pages",
  "journal": "Indiana Journal of Mathematics, 50 (2001) no. 4, 1867-1883",
  "categories": [
    "math.DG"
  ],
  "abstract": "This paper concerns complete noncompact manifolds with nonnegative Ricci curvature. Roughly, we say that M has the loops to infinity property if given any noncontractible closed curve, C, and given any compact set, K, there exists a closed curve contained in M\\K which is homotopic to C. The main theorems in this paper are the following. Theorem I: If M has positive Ricci curvature then it has the loops to infinity property. Theorem II: If M has nonnegative Ricci curvature then it either has the loops to infinity property or it is isometric to a flat normal bundle over a compact totally geodesic submanifold and its double cover is split. Theorem III: Let M be a complete riemannian manifold with the loops to infinity property along some ray starting at a point, p. Let D containing p be a precompact region with smooth boundary and S be any connected component of the boundary containing a point, q, on the ray. Then the map from the fundamental group of S based at q to the fundamental group of Cl(D) based at p induced by the inclusion map is onto.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-04-19T17:12:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnegative ricci curvature",
      "fundamental group",
      "loops representing elements",
      "infinity property",
      "complete manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......4096S"
    }
  }
}