1 1 Ju l 2 00 4 Some isometry groups of Urysohn space
نویسنده
چکیده
We construct various isometry groups of Urysohn space (the unique complete separable metric space which is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.
منابع مشابه
Some isometry groups of Urysohn space
We construct various isometry groups of Urysohn space (the unique complete separable metric space that is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.
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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 H 2 b (Γ, R), H 2 b (Γ, ℓ p (Γ)) (1 ≤ p < ∞) are infinite dimensional. Our result holds for example for any subgroup of the mapping c...
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