{
  "id": "1710.05498",
  "version": "v1",
  "published": "2017-10-16T04:11:50.000Z",
  "updated": "2017-10-16T04:11:50.000Z",
  "title": "Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups",
  "authors": [
    "Jiayin Pan"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature. We show that if there is an integer $k$ such that any tangent cone at infinity of the Riemannian universal cover of $M$ is a metric cone, whose maximal Euclidean factor has dimension $k$, then $\\pi_1(M)$ is finitely generated. In particular, this confirms the Milnor conjecture for an manifold whose universal cover has Euclidean volume growth and the unique tangent cone at infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T04:11:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnegative ricci curvature",
      "fundamental group",
      "finite generation",
      "unique tangent cone",
      "euclidean volume growth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}