Bounded cohomology and isometry groups of hyperbolic spaces

  title={Bounded cohomology and isometry groups of hyperbolic spaces},
  author={Ursula Hamenst¨adt},
  • Ursula Hamenst¨adt
  • Published 2005
Let X be an arbitrary hyperbolic geodesic metric space and let 0 be a countable subgroup of the isometry group Iso (X) of X. We show that if0 is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups H2 b (0,R), H2 b (0, `p(0)) (1 < p < ∞) 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… CONTINUE READING

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