Sharp, Richard
(2007)
*Critical exponents for groups of isometries.*
Geometriae Dedicata, 125 (1).
pp. 63-74.
ISSN 1572-9168

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Official URL: http://www.springerlink.com/content/q9327h276178/?...

## Abstract

Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ_0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ_0 to have the same critical exponent is that Γ / Γ_0 is amenable.

Item Type: | Article |
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Uncontrolled Keywords: | CAT(−1)space - Riemannian manifold - Negative curvature - Group of isometrics - Critical exponent - Amenable group |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 20 Nov 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/925 |

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