Skip to main content
eScholarship
Open Access Publications from the University of California

UC Santa Barbara

UC Santa Barbara Previously Published Works bannerUC Santa Barbara

Describing the universal cover of a compact limit

Abstract

If X is the Gromov-Hausdorff limit of a sequence of Riemannian manifolds M-i(n) with a uniform lower bound on Ricci curvature, Sormani and Wei have shown that the universal cover of (X) over bar exists [C. Sormani, G. Wei, Hausdorff convergence and universal covers, Trans. Amer. Math. Soc. 353 (9) (2001) 3585-3602 (electronic)]; [C. Sormani, G. Wei, Universal covers for Hausdorff limits of noncompact spaces, Trans. Amer. Math. Soc. 356 (3) (2004) 1233-1270 (electronic). [15]]. For the case where X is compact, we provide a description of (X) over tilde in terms of the universal covers (M) over tilde (i) of the manifolds. More specifically we show that if X is the pointed Gromov-Hausdorff limit of the universal covers (M) over tilde (i) then there is a subgroup H of Iso((X) over bar) such that (X) over bar = (X) over bar /H. We call H the small action limit group and prove a similar result for compact length spaces with uniformly bounded dimension. (C) 2006 Elsevier B.V. All rights reserved.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View