The codimension one homology of a complete manifold with nonnegative Ricci curvature

1999/09/30 by Zhongmin Shen, Christina Sormani · 1 citation
Mathematics · #math.DG #math.MG #msc:53C20

paper · pdf

published as American Journal of Mathematics, 123(2001), 515-524. · Revised Version, 10 pages, 5 figures, Amer. J. Math. (to appear)

arxiv created 2000/11/18 · arxiv updated 2009/11/30

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.

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