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 π1(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.

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