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2007.181: Critical exponents for groups of isometries

2007.181: Richard Sharp (2007) Critical exponents for groups of isometries. Geometriae Dedicata, 125 (1). pp. 63-74. ISSN 1572-9168

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DOI: 10.1007/s10711-007-9137-9


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 2000 > 20 Group theory and generalizations
MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2007.181
Deposited By:Mrs Louise Healey
Deposited On:20 November 2007

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