Isometry groups of proper CAT(0)-spaces of rank one
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).
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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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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 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).
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2012
ISSN: 1661-7207
DOI: 10.4171/ggd/166