The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Emery Ricci curvature.

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative N-Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative N-Bakry Émery Ricci curvature. In addition, we show that if Mⁿ is a complete, noncompact Riemannian manifold with nonnegative N-Bakry Émery Ricci curvature where N > n, then H_n−1(M,Z) is 0. [ABSTRACT FROM AUTHOR]