Describing the universal cover of a noncompact limit

摘要

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 X is a quotient of the Gromov-Hausdorff limit of the universal covers 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.