On the bounded cohomology of ergodic group actions

TL;DR

This paper demonstrates the existence of bounded cocycles with specific properties over certain group actions, advancing understanding in the area of bounded cohomology and ergodic theory.

Contribution

It establishes the existence of bounded, transitive cocycles over finitely generated groups and bounded, ergodic cocycles over a5^d actions, providing new examples in bounded cohomology.

Findings

Existence of bounded, transitive cocycles over finitely generated groups

Existence of bounded, ergodic cocycles over a5^d actions

Advancement in understanding of bounded cohomology in ergodic group actions

Abstract

In this note we show existence of bounded, transitive cocycles over a transitive action of a finitely generated group, and bounded, ergodic cocycles over an ergodic, probability preserving action of $\Bbb Z^d$.