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

 

Group completions and orbifolds of variable negative curvature


Author: Christopher W. Stark
Journal: Proc. Amer. Math. Soc. 114 (1992), 191-194
MSC: Primary 57S30; Secondary 53C21
MathSciNet review: 1079709
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Abstract: W. J. Floyd's comparison of the Furstenberg maximal boundary of a noncompact, $ {\mathbf{R}}$-rank one, connected semisimple Lie group $ G$ with finite center and the group completion of a discrete, cocompact subgroup $ \Gamma $ of $ G$ is extended to a homeomorphism between the group completion of the fundamental group $ \Gamma $ of a closed Riemannian orbifold $ M = \Gamma \backslash X$ of strictly negative sectional curvatures and the sphere at infinity in the Eberlein-O'Neill compactification $ \overline X $ of the universal cover $ X$ of $ M$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079709-0
PII: S 0002-9939(1992)1079709-0
Keywords: Discrete groups, sphere at infinity, negative curvature, group completion, Rauch comparison theorem
Article copyright: © Copyright 1992 American Mathematical Society