Ideal bicombings for hyperbolic groups and applications

Details Ideal bicombings for hyperbolic groups and applications Ideal bicombings for hyperbolic groups and applications

2003-04-19

arxiv.org/abs/math/0304278v2

Mathematics

Group Theory

Substantial generalizeation; now the results hold for a general class of hyperbolic metric spaces (rather than just hyperbolic

Scientific paper

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.

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