• Corpus ID: 18105882

Bounded cohomology, cross ratios and cocycles

@article{Hamenstaedt2005BoundedCC,
  title={Bounded cohomology, cross ratios and cocycles},
  author={Ursula Hamenstaedt},
  journal={arXiv: Group Theory},
  year={2005}
}
We use cross ratios to describe second real continuous bounded cohomology for locally compact topological groups. We also derive a rigidity result for cocycles with values in the isometry group of a proper hyperbolic geodesic metric space. 
View PDF on arXiv
3 Citations

3 Citations

Citation Type

Citation Type

Isometry Groups of Proper Hyperbolic Spaces
Abstract.Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second…
Isometry groups of proper hyperbolic spaces
Let X be a proper hyperbolic geodesic metric space of bounded growth and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not amenable then the second continuous…
Geometry of the mapping class groups I: Boundary amenability
We construct a geometric model for the mapping class group $\mathcal{M}\mathcal{C}\mathcal{G}$ of a non-exceptional oriented surface S of genus g with k punctures and use it to show that the action…

References

SHOWING 1-10 OF 17 REFERENCES
Cocycle superrigidity and bounded cohomology for negatively curved spaces
We introduce new techniques to extend superrigidity theory beyond the scope of Lie or algebraic groups. We construct a cohomological invariant which accounts for, and generalizes, all known…
Continuous bounded cohomology of locally compact groups
We introduce and study the theory of continuous bounded cohomology of topological groups with coefficients in Banach modules. This encompasses the bounded cohomology of abstract groups as a special…
Isometry Groups of Proper Hyperbolic Spaces
Abstract.Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second…
Ideal bicombings for hyperbolic groups and applications
Orbit equivalence rigidity and bounded cohomology
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide…
Reduction of cocycles with hyperbolic targets
  • S. Adams
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1996
Abstract We show that any cocycle from an ergodic, finite measure preserving action of a higher-rank group to a closed subgroup of the isometry group of a proper, geodesic hyperbolic, ‘at most…
Bounded cohomology of lattices in higher rank Lie groups
We prove that the natural map Hb2(Γ)?H2(Γ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial…
Foundations of the theory of bounded cohomology
In this paper we give a new approach to the theory of bounded cohomology. The ideas of relative homological algebra, modified so that they are based on a natural seminorm in the bounded cohomology,…
Continuous bounded cohomology and applications to rigidity theory
We present a theory of continuous bounded cohomology of locally compact groups with coefficients in Banach modules. A central role is played by amenable actions, as they give rise to relatively…
BOUNDED COHOMOLOGY THEORY AND APPLICATIONS TO DEFORMATION RIGIDITY IN COMPLEX HYPERBOLIC GEOMETRY
We develop further basic tools in the theory of bounded continuous cohomology of locally compact groups; as such, this paper can be considered a sequel to [18], [39], and [11]. In particular: we…
...
1
2
...