ar X iv : m at h / 03 04 27 8 v 1 [ m at h . G R ] 1 9 A pr 2 00 3 IDEAL BICOMBINGS FOR HYPERBOLIC GROUPS AND APPLICATIONS
نویسنده
چکیده
For every hyperbolic group, we construct an ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [26] hold for all non-elementary hyperbolic groups and their non-elementary subgroups. For any subgroup Γ of a hyperbolic group, this invariant provides a class in H2b(Γ, l (Γ)) which vanishes if and only if Γ is elementary. As an additional application, we derive a superrigidity result for homomorphisms of general irreducible lattices to hyperbolic groups.
منابع مشابه
ar X iv : m at h / 03 04 27 8 v 2 [ m at h . G R ] 1 5 M ay 2 00 3 IDEAL BICOMBINGS FOR HYPERBOLIC GROUPSAND APPLICATIONS
For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all non-elementary hyperbolic groups and thei...
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