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Nonnegative Ricci curvature, metric cones and virtual abelianness

Jiayin Pan

Geometry & Topology 28 (2024) 1409–1436
Abstract

Let M be an open n–manifold with nonnegative Ricci curvature. We prove that if its escape rate is not 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 π1(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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