Mineyev, IgorMonod, NicolasShalom, Yehuda2008-10-292008-10-292008-10-29200410.1016/j.top.2004.01.008https://infoscience.epfl.ch/handle/20.500.14299/30484For 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 by Monod–Shalom hold for all non-elementary hyperbolic groups and their non-elementary subgroups. We also derive superrigidity results for actions of general irreducible lattices on a large class of hyperbolic metric spaces.text::journal::journal article::research article