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Universal covers for Hausdorff limits of noncompact spaces
Authors:
Christina Sormani and Guofang Wei
Journal:
Trans. Amer. Math. Soc. 356 (2004), 1233-1270
MSC (2000):
Primary 53C20
Posted:
October 6, 2003
MathSciNet review:
2021619
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Abstract: We prove that if is the Gromov-Hausdorff limit of a sequence of complete manifolds, , with a uniform lower bound on Ricci curvature, then has a universal cover.
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- M. Anderson, On the topology of complete manifolds of non-negative Ricci curvature, Topology 29 (1990), no. 1, 41-55. MR 91b:53041
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- R. Bishop, R. Crittenden, Geometry of manifolds. Reprint of the 1964 original. AMS Chelsea Publishing, Providence, RI, 2001. MR 2002d:53001
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- B.H. Bowditch, G. Mess, A
-dimensional Kleinian group. Trans. Amer. Math. Soc. 344 (1994), no. 1, 391-405. MR 95f:57057
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- J. Cheeger, T. Colding, On the structure of spaces with Ricci curvature bounded below I, J. Diff. Geom. 46 (1997) 406-480. MR 98k:53044
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- J. Milnor, A note on curvature and fundamental group, J. Diff. Geom. 2 (1968) 1-7. MR 38:636
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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/S0002-9947-03-03412-3
PII:
S 0002-9947(03)03412-3
Received by editor(s):
July 24, 2002
Received by editor(s) in revised form:
February 28, 2003
Posted:
October 6, 2003
Additional Notes:
The first author was partially supported by NSF Grant # DMS-0102279 and a grant from The City University of New York PSC-CUNY Research Award Program
The second author was partially supported by NSF Grant # DMS-9971833
Article copyright:
© Copyright 2003 American Mathematical Society
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