  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.
