# 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.

## 3 Citations

Isometry Groups of Proper Hyperbolic Spaces

- Mathematics
- 2005

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

- Mathematics
- 2005

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

- Mathematics
- 2005

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 16 REFERENCES

Cocycle superrigidity and bounded cohomology for negatively curved spaces

- Mathematics
- 2004

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

- Mathematics
- 2000

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

- Mathematics
- 2005

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…

Orbit equivalence rigidity and bounded cohomology

- Mathematics
- 2006

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

- Mathematics
- 1996

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 exponential’…

Bounded cohomology of lattices in higher rank Lie groups

- Mathematics
- 1999

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…

Bounded cohomology and isometry groups of hyperbolic spaces

- Mathematics
- 2006

Let X be an arbitrary hyperbolic geodesic metric space and let 0 be a countable sub- group of the isometry group Iso(X) ofX. We show that if0 is non-elementary and weakly acylin- drical (this is a…

Foundations of the theory of bounded cohomology

- Mathematics
- 1987

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

- Mathematics
- 2001

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…