Ideal bicombings for hyperbolic groups and applications.

DOI10.1016/j.top.2004.01.008zbMath1137.20033arXivmath/0304278OpenAlexW3104219058MaRDI QIDQ1888450

Igor Mineyev, Nicolas Monod, Yehuda Shalom

Publication date: 23 November 2004

Published in: Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0304278

zbMATH Keywords

hyperbolic spaceshyperbolic groupshyperbolic graphsbounded cohomologycohomological invariantssuperrigiditynegatively curved manifoldsideal bicombingsnon-elementary subgroups

Mathematics Subject Classification ID

Geometric group theory (20F65) Cohomology of groups (20J06) Topological methods in group theory (57M07) Hyperbolic groups and nonpositively curved groups (20F67) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) General groups of measure-preserving transformations and dynamical systems (37A15) Measurable group actions (22F10)

Related Items

Extending higher-dimensional quasi-cocycles ⋮ Relative bounded cohomology for groupoids ⋮ Flows and joins of metric spaces ⋮ Induced quasicocycles on groups with hyperbolically embedded subgroups. ⋮ Rigidity for von Neumann algebras given by locally compact groups and their crossed products ⋮ Amenable hyperbolic groups ⋮ Bounded cohomology and isometry groups of hyperbolic spaces ⋮ On the structural theory of \(\mathrm{II}_1\) factors of negatively curved groups. II: Actions by product groups ⋮ Negative curvature from a cohomological viewpoint and cocycle superrigidity ⋮ Isometry groups of proper CAT(0)-spaces of rank one. ⋮ On strong property (T) and fixed point properties for Lie groups ⋮ Fixed point property for universal lattice on Schatten classes ⋮ A lattice in more than two Kac-Moody groups is arithmetic. ⋮ Superrigidity of hyperbolic buildings ⋮ Dehn filling in relatively hyperbolic groups. ⋮ Geometry of the mapping class groups. I: Boundary amenability ⋮ The median class and superrigidity of actions on CAT(0) cube complexes ⋮ Inner amenability for groups and central sequences in factors ⋮ Simplicity and superrigidity of twin building lattices. ⋮ Low degree bounded cohomology and \(L^{2}\)-invariants for negatively curved groups ⋮ Isometry groups of non-positively curved spaces: discrete subgroups ⋮ Singularities, expanders and topology of maps. I: Homology versus volume in the spaces of cycles