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Critical exponents for groups of isometries |
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| Authors: | Richard Sharp |
| Institution: | (1) School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, U.K. |
| Abstract: | Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ / Γ0 is amenable. |
| Keywords: | CAT(− 1)space Riemannian manifold Negative curvature Group of isometrics Critical exponent Amenable group |
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