On the bounded cohomology of ergodic group actions. (English) Zbl 1461.37005
The authors show the existence of bounded, continuous, transitive cocycles over a transitive action by homeomorphisms of any finitely generated group on a Polish space and of bounded, measurable, ergodic cocycles over any ergodic, probability-preserving action of \({\mathbb Z}^d\). A few open problems show that the techniques cannot be easily generalized or adapted to more general situations.
Reviewer: George Stoica (Saint John)
MSC:
| 37A15 | General groups of measure-preserving transformations and dynamical systems |
| 37A20 | Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations |
| 28D15 | General groups of measure-preserving transformations |
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