an:05575933
Zbl 1273.53037
Hamenstädt, Ursula
Isometry groups of proper hyperbolic spaces
EN
Geom. Funct. Anal. 19, No. 1, 170-205 (2009).
1016-443X 1420-8970
2009
j
53C24 20F67 20J06
hyperbolic spaces; isometry groups; bounded cohomology
Summary: Let \(X\) be a proper hyperbolic geodesic metric space and let \(G\) be a closed subgroup of the isometry group \(\text{Iso}(X)\) of \(X\). We show that if \(G\) is not elementary then for every \(p\in (1,\infty)\) the second continuous bounded cohomology group \(H^2_{cb}(G,L^p(G))\) does not vanish. As an application, we derive some structure results for closed subgroups of \(\text{Iso}(X)\).