2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79052In 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.Revised Version, 10 pages, 5 figures, Amer. J. Math. (to appear)Differential GeometryMetric Geometry53C20text