Critical Exponents for Groups of Isometries

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. 0. Introduction and Results Let Γ be a group of isometries acting freely and properly discontinuously on a CAT… CONTINUE READING