On the fundamental group of noncompact manifolds with nonnegative Ricci curvature

We study the fundamental group of noncompact Riemannian manifolds with nonnegative Ricci curvature. We show that the fundamental group of a noncompact, complete, Riemannian manifold with nonnegative Ricci curvature and small linear diameter growth is almost the fundamental group of a large ball. We make this precise by studying semi-local fundamental groups. We also find relationships between the semi-local fundamental groups and special Gromov-Hausdorff limits of a manifold called tangent cones at infinity. As an application we show that any tangent cone at infinity of a complete open manifold with nonnegative Ricci curvature and small linear diameter growth is its own universal cover.; We also derive bounds on the number of generators of the fundamental group for some families of complete open manifolds with nonnegative Ricci curvature. In fact we show that the fundamental group of these manifolds behaves somewhat like the fundamental group of a compact manifold. We also show there is a relationship between the volume growth of a manifold with nonnegative Ricci curvature and the length of a loop representing an element of infinite order in pi1(M).