Critical exponents for groups of isometries

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

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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
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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