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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Describing the universal cover of a noncompact limit

John Ennis and Guofang Wei

Geometry & Topology 14 (2010) 2479–2496
Abstract

Suppose that X is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds Min with a uniform lower bound on Ricci curvature. In a previous paper the authors showed that when X is compact the universal cover X̃ is a quotient of the Gromov–Hausdorff limit of the universal covers M̃in. This is not true when X is noncompact. In this paper we introduce the notion of pseudo-nullhomotopic loops and give a description of the universal cover of a noncompact limit space in terms of the covering spaces of balls of increasing size in the sequence.

Keywords
universal cover, Gromov–Hausdorff limit
Mathematical Subject Classification 2000
Primary: 53C20
References
Publication
Received: 2 August 2007
Revised: 6 May 2010
Accepted: 17 October 2010
Published: 10 December 2010
Proposed: Gang Tian
Seconded: Tobias H Colding, Steven Ferry
Authors
John Ennis
The Institute for Perception
7629 Hull Street Rd
Richmond VA 23235
USA
Guofang Wei
Mathematics Department
University of California, Santa Barbara
Santa Barbara CA 93106
USA