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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lipschitz precompactness
for closed negatively curved manifolds


Author: Igor Belegradek
Journal: Proc. Amer. Math. Soc. 127 (1999), 1201-1208
MSC (1991): Primary 53C20, 53C23; Secondary 20F32, 57R55
MathSciNet review: 1476116
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Abstract: We prove that, given a integer $n\ge 3$ and a group $\pi $, the class of closed Riemannian $n$-manifolds of uniformly bounded negative sectional curvatures and with fundamental groups isomorphic to $\pi $ is precompact in the Lipschitz topology. In particular, the class breaks into finitely many diffeomorphism types.


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Additional Information

Igor Belegradek
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Address at time of publication: Department of Mathematics and Statistics, McMaster University, 1280 Main St. West, Hamilton, Ontario, Canada L8S 4K1
Email: igorb@math.umd.edu, belegi@icarus.math.mcmaster.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04654-7
PII: S 0002-9939(99)04654-7
Keywords: Lipschitz convergence, negatively curved manifold
Received by editor(s): July 30, 1997
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society