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

Zhongmin Shen; Christina Sormani

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arXiv · math/9909017

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

Zhongmin Shen·Christina Sormani

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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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Zhongmin Shen, Christina Sormani. 2000-11-18. The codimension one homology of a complete manifold with nonnegative Ricci curvature. https://arxiv.org/abs/math/9909017

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