Abstract
Suppose that is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds with a uniform lower bound on Ricci curvature. In a previous paper the authors showed that when is compact the universal cover is a quotient of the Gromov–Hausdorff limit of the universal covers . This is not true when 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.
Citation
John Ennis. Guofang Wei. "Describing the universal cover of a noncompact limit." Geom. Topol. 14 (4) 2479 - 2496, 2010. https://doi.org/10.2140/gt.2010.14.2479
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