Ideal bicombings for hyperbolic groups and 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 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.


Published in:
Topology, 43, 6, 1319-1344
Year:
2004
Laboratories:




 Record created 2008-10-29, last modified 2018-03-17


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