{
  "id": "math/9909017",
  "version": "v2",
  "published": "1999-09-02T18:37:11.000Z",
  "updated": "2000-11-18T19:50:08.000Z",
  "title": "The codimension one homology of a complete manifold with nonnegative Ricci curvature",
  "authors": [
    "Zhongmin Shen",
    "Christina Sormani"
  ],
  "comment": "Revised Version, 10 pages, 5 figures, Amer. J. Math. (to appear)",
  "journal": "American Journal of Mathematics, 123(2001), 515-524.",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "In this paper we prove that a complete noncompact manifold with nonnegative Ricci curvature has a trivial codimension one homology unless it is a split or flat normal bundle over a compact totally geodesic submanifold. In particular, we prove the conjecture that a complete noncompact manifold with positive Ricci curvature has a trivial codimension one integer homology. We also have a corollary stating when the codimension two integer homology of such a manifold is torsion free.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-11-18T19:50:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "nonnegative ricci curvature",
      "complete manifold",
      "complete noncompact manifold",
      "integer homology",
      "trivial codimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......9017S"
    }
  }
}