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The codimension one homology of a complete manifold with nonnegative Ricci curvature
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 123, Number 3, June 2001
- pp. 515-524
- 10.1353/ajm.2001.0020
- Article
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In this paper we prove that a complete noncompact manifold with nonnegative Ricci curvature has a trivial codimension one homology unless it is a 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.