Nonnegative Ricci curvature, metric cones and virtual abelianness

Pan, Jiayin

doi:10.2140/gt.2024.28.1409

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Nonnegative Ricci curvature, metric cones and virtual abelianness

Jiayin Pan

Geometry & Topology 28 (2024) 1409–1436

DOI: 10.2140/gt.2024.28.1409

Abstract

Let $M$ be an open $n$ –manifold with nonnegative Ricci curvature. We prove that if its escape rate is not $\frac{1}{2}$ and its Riemannian universal cover is conic at infinity (that is, every asymptotic cone $(Y, y)$ of the universal cover is a metric cone with vertex $y$ ), then $π_{1} (M)$ contains an abelian subgroup of finite index. If in addition the universal cover has Euclidean volume growth of constant at least $L$ , we can further bound the index by a constant $C (n, L)$ .

Keywords

Ricci curvature, fundamental groups

Mathematical Subject Classification

Primary: 53C20, 53C23

Secondary: 53C21, 57S30

References

Publication

Received: 3 February 2022

Revised: 7 July 2022

Accepted: 5 August 2022

Published: 10 May 2024

Proposed: Tobias H Colding

Seconded: David Fisher, Urs Lang

Authors

Jiayin Pan
Fields Institute for Research in Mathematical Sciences Toronto, ON Canada	Mathematics Department University of California, Santa Cruz Santa Cruz, CA United States

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Volume 28, issue 3 (2024)