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Ideal bicombings for hyperbolic groups and applications

I. Mineyev·N. Monod·Y. Shalom
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Abstract

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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I. Mineyev, N. Monod, Y. Shalom. 2003-05-15. Ideal bicombings for hyperbolic groups and applications. https://doi.org/10.1016/j.top.2004.01.008

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