Describing the universal cover of a noncompact limit

Ennis, John; Wei, Guofang

doi:10.2140/gt.2010.14.2479

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Describing the universal cover of a noncompact limit

John Ennis and Guofang Wei

Geometry & Topology 14 (2010) 2479–2496

DOI: 10.2140/gt.2010.14.2479

Abstract

Suppose that $X$ is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds $M_{i}^{n}$ with a uniform lower bound on Ricci curvature. In a previous paper the authors showed that when $X$ is compact the universal cover $\tilde{X}$ is a quotient of the Gromov–Hausdorff limit of the universal covers ${\tilde{M}}_{i}^{n}$ . 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

Volume 14, issue 4 (2010)