Nonnegative Ricci curvature, stability at infinity and finite generation of fundamental groups

摘要

We study the fundamental group of an open n-manifold M of nonnegative Ricci curvature. We show that if there is an integer k such that any tangent cone at infinity of the Riemannian universal cover of M is a metric cone whose maximal Euclidean factor has dimension k, then pi(1) (M) is finitely generated. In particular, this confirms the Milnor conjecture for a manifold whose universal cover has Euclidean volume growth and a unique tangent cone at infinity.