{
  "id": "0801.2216",
  "version": "v2",
  "published": "2008-01-15T05:45:47.000Z",
  "updated": "2008-08-25T06:52:10.000Z",
  "title": "Knots in Riemannian manifolds",
  "authors": [
    "Fuquan Fang",
    "S. Mendonca"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "In this paper we study submanifold with nonpositive extrinsic curvature in a positively curved manifold. Among other things we prove that, if $K\\subset (S^n, g)$ is a totally geodesic submanifold in a Riemannian sphere with positive sectional curvature where $n\\ge 5$, then $K$ is homeomorphic to $S^{n-2}$ and the fundamental group of the knot complement $\\pi_1(S^n-K)\\cong \\Bbb Z$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-25T06:52:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian manifolds",
      "study submanifold",
      "fundamental group",
      "nonpositive extrinsic curvature",
      "positive sectional curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2216F"
    }
  }
}