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

Pan, Jiayin

doi:10.2140/gt.2019.23.3203

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

Jiayin Pan

Geometry & Topology 23 (2019) 3203–3231

DOI: 10.2140/gt.2019.23.3203

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 $π_{1} (M)$ 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.

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Keywords

Ricci curvature, fundamental groups

Mathematical Subject Classification 2010

Primary: 53C20, 53C23

Secondary: 53C21, 57S30

References

Publication

Received: 8 October 2018

Revised: 2 March 2019

Accepted: 2 April 2019

Published: 1 December 2019

Proposed: Tobias H Colding

Seconded: Bruce Kleiner, John Lott

Authors

Jiayin Pan
Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States

Volume 23, issue 6 (2019)