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 ${\pi }_1(M)$ is finitely generated. In particular, this confirms the Milnor conjecture for a manifold whose universal cover has Euclidean volume growth and the unique tangent cone at infinity.

References in corpus (1)

• A Proof of Milnor conjecture in dimension 3

Cited by in corpus (7)

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• Nonnegative Ricci curvature, splitting at infinity, and first Betti number rigidity
• Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups