Length functions and parameterizations of Teichmüller space for surfaces with cusps.
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....
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