#### Volume 23, issue 6 (2019)

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

### Jiayin Pan

Geometry & Topology 23 (2019) 3203–3231
##### 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.

##### Keywords
Ricci curvature, fundamental groups
##### Mathematical Subject Classification 2010
Primary: 53C20, 53C23
Secondary: 53C21, 57S30