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

DOI:
https://doi.org/10.1090/S0002-9939-99-04654-7

MathSciNet review:
1476116

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that, given a integer and a group , the class of closed Riemannian -manifolds of uniformly bounded negative sectional curvatures and with fundamental groups isomorphic to 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:
https://doi.org/10.1090/S0002-9939-99-04654-7

Keywords:
Lipschitz convergence,
negatively curved manifold

Received by editor(s):
July 30, 1997

Communicated by:
Christopher Croke

Article copyright:
© Copyright 1999
American Mathematical Society