Isometry groups of proper hyperbolic spaces

Details Isometry groups of proper hyperbolic spaces Isometry groups of proper hyperbolic spaces

2005-07-29

arxiv.org/abs/math/0507608v4

Mathematics

Group Theory

30 pages; writing improved, details added. Combined with parts of math.GR/0508532. To appear in GAFA

Scientific paper

Let X be a proper hyperbolic geodesic metric space and let G be a closed
subgroup of the isometry group Iso(X) of X. We show that if G is not amenable
then its second continuous bounded cohomology group with coefficients the
regular representation does not vanish. This yields some structure results for
such groups.

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