Let be an arbitrary hyperbolic geodesic metric space and let be a countable subgroup of the isometry group of . We show that if is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups , are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct product.
Cite this article
Ursula Hamenstädt, Bounded cohomology and isometry groups of hyperbolic spaces. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 315–349DOI 10.4171/JEMS/112