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On the fundamental groups of negatively curved manifolds with finite volume

Author: Midori S. Goto
Journal: Proc. Amer. Math. Soc. 75 (1979), 99-103
MSC: Primary 53C20; Secondary 22E40
MathSciNet review: 529223
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Abstract: We will prove that if M is a complete, simply connected riemannian manifold with sectional curvature K, $ a \leqslant K < 0$, for $ a > 0$ and $ \Gamma $ a properly discontinuous group of isometries of M acting freely on M with volume $ (M/\Gamma )$ finite, then $ M/\Gamma $ is compact if and only if $ \Gamma $ consists of hyperbolic elements.

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Keywords: Fundamental group, negatively curved manifold, hyperbolic isometry, Dirichlet region
Article copyright: © Copyright 1979 American Mathematical Society

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