Ideal bicombings for hyperbolic groups and applications

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.

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

References in corpus (1)

• Some prime factorization results for type II_1 factors

Cited by in corpus (12)

• Simplicity and superrigidity of twin building lattices
• Induced quasi-cocycles on groups with hyperbolically embedded subgroups
• On the structural theory of II_1 factors of negatively curved groups, II: Actions by product groups
• The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes
• Isometry groups of non-positively curved spaces: discrete subgroups
• Flows and joins of metric spaces
• A lattice in more than two Kac--Moody groups is arithmetic
• Extending higher dimensional quasi-cocycles
• Inner amenability for groups and central sequences in factors
• Primeness results for von Neumann algebras associated with surface braid groups
• Rigidity for von Neumann algebras given by locally compact groups and their crossed products
• Relative Bounded Cohomology for Groupoids