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

Abstract

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 ${\pi }_1\left(M\right)$ 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.