Hausdorff convergence and universal covers
Authors:
Christina Sormani and Guofang Wei
Journal:
Trans. Amer. Math. Soc. 353 (2001), 35853602
MSC (1991):
Primary 53C20
Published electronically:
April 26, 2001
MathSciNet review:
1837249
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Abstract: We prove that if is the GromovHausdorff limit of a sequence of compact manifolds, , with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then has a universal cover. We then show that, for sufficiently large, the fundamental group of has a surjective homeomorphism onto the group of deck transforms of . Finally, in the noncollapsed case where the have an additional uniform lower bound on volume, we prove that the kernels of these surjective maps are finite with a uniform bound on their cardinality. A number of theorems are also proven concerning the limits of covering spaces and their deck transforms when the are only assumed to be compact length spaces with a uniform upper bound on diameter.
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Additional Information
Christina Sormani
Affiliation:
Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, New York 10468
Email:
sormani@g230.lehman.cuny.edu
Guofang Wei
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106
Email:
wei@math.ucsb.edu
DOI:
http://dx.doi.org/10.1090/S0002994701028021
PII:
S 00029947(01)028021
Received by editor(s):
September 6, 2000
Published electronically:
April 26, 2001
Additional Notes:
Partially supported by NSF Grant #DMS9971833
Article copyright:
© Copyright 2001 American Mathematical Society
