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Isometry groups of proper hyperbolic spaces

Ursula Hamenstadt
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Abstract

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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Ursula Hamenstadt. 2008-03-16. Isometry groups of proper hyperbolic spaces. https://arxiv.org/abs/math/0507608

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