The codimension one homology of a complete manifold with nonnegative Ricci curvature
Differential Geometry
2007-05-23 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/9909017,
title = {The codimension one homology of a complete manifold with nonnegative Ricci curvature},
author = {Zhongmin Shen and Christina Sormani},
journal= {arXiv preprint arXiv:math/9909017},
year = {2007}
}
Comments
Revised Version, 10 pages, 5 figures, Amer. J. Math. (to appear)