Isometry Groups of Proper Hyperbolic Spaces
نویسندگان
چکیده
منابع مشابه
5 Isometry Groups of Proper Hyperbolic Spaces
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 elementary then for every p ∈ [1, ∞) the second continuous bounded cohomology group H 2 cb (G, L p (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).
متن کامل. G R ] 3 0 Ju l 2 00 6 ISOMETRY GROUPS OF PROPER HYPERBOLIC SPACES
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 elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H 2 cb (G, L p (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).
متن کامل. G R ] 2 9 Ju l 2 00 5 ISOMETRY GROUPS OF PROPER HYPERBOLIC SPACES
Let X be a proper hyperbolic geodesic metric space of bounded growth and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not amenable then the second continuous bounded cohomol-ogy group H 2 cb (G, L 2 (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).
متن کامل. G R ] 1 6 M ar 2 00 8 ISOMETRY GROUPS OF PROPER HYPERBOLIC SPACES
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 elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H 2 cb (G, L p (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).
متن کاملIsometry Groups of Proper Cat
Let X be a proper CAT(0)-space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is non-elementary and contains a rank-one element then its second bounded cohomology group with coefficients in the regular representation is non-trivial. As a consequence, up to passing to an open subgroup of finite index, either G is a compact extension of a totally disconnected ...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2009
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-009-0719-6