{
  "id": "math/9809133",
  "version": "v1",
  "published": "1998-09-23T18:13:41.000Z",
  "updated": "1998-09-23T18:13:41.000Z",
  "title": "Nonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groups",
  "authors": [
    "Christina Sormani"
  ],
  "comment": "12 pages, figures available from author sormani@math.jhu.edu",
  "journal": "Journal of Differential Geom. 54 (2000), no. 3, 547--559",
  "categories": [
    "math.DG"
  ],
  "abstract": "In 1968, Milnor conjectured that a complete noncompact manifold with nonnegative Ricci curvature has a finitely generated fundamental group. The author applies the Excess Theorem of Abresch and Gromoll (1990), to prove two theorems. The first states that if such a manifold has small linear diameter growth then its fundamental group is finitely generated. The second states that if such a manifold has an infinitely generated fundamental group then it has a tangent cone at infinity which is not polar. A corollary of either theorem is the fact that if such a manifold has linear volume growth, then its fundamental group is finitely generated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-23T18:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21"
    ],
    "keywords": [
      "small linear diameter growth",
      "nonnegative ricci curvature",
      "finite generation",
      "generated fundamental group",
      "linear volume growth"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......9133S"
    }
  }
}