Critical exponents for groups of isometries
Copyright policy )Critical exponents for groups of isometries
Let \(\Gamma\) be a free group acting by isometries on a \(\text{CAT}(-1)\) space \((X,d_X)\) as a convex co-compact group and let \(\Gamma_0\) be a normal subgroup. The author shows that if the quotient group \(\Gamma/\Gamma_0\) is amenable, then \(\delta(\Gamma_0)=\delta(\Gamma)\). Here \(\delta(G)\) denotes the critical exponent associated to the group \(G\). The result is applied to Kleinian groups and, in particular, to finitely generated Fuchsian groups.
- University of Salford United Kingdom
Orbit growth in dynamical systems, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, convex groups, Means on groups, semigroups, etc.; amenable groups, co-compact groups, \(\text{CAT}(-1)\) spaces, negative curvature, random walks, co-growth of groups, Hyperbolic groups and nonpositively curved groups, Asymptotic properties of groups, amenable groups, critical exponents, groups of isometries
Orbit growth in dynamical systems, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, convex groups, Means on groups, semigroups, etc.; amenable groups, co-compact groups, \(\text{CAT}(-1)\) spaces, negative curvature, random walks, co-growth of groups, Hyperbolic groups and nonpositively curved groups, Asymptotic properties of groups, amenable groups, critical exponents, groups of isometries
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