Geodesic
Bounded cohomology and isometry groups of hyperbolic spaces
Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 315-349

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Let X be an arbitrary hyperbolic geodesic metric space and let Γ be a countable subgroup of the isometry group Iso(X) of X. We show that if Γ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups Hb2​(Γ,R), Hb2​(Γ,lp(Γ)) (1∞) 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.
DOI : 10.4171/jems/112
Classification : 58-XX, 00-XX
Keywords: 
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     author = {Ursula Hamenst\"adt},
     title = {Bounded cohomology and isometry groups of hyperbolic spaces},
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Ursula Hamenstädt. Bounded cohomology and isometry groups of hyperbolic spaces. Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 315-349. doi: 10.4171/jems/112

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