On the bounded cohomology for ergodic nonsingular actions of amenable groups

Alexandre I. Danilenko

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arXiv · 1909.00620

On the bounded cohomology for ergodic nonsingular actions of amenable groups

Alexandre I. Danilenko

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Abstract

Let $\Gamma$ be an amenable countable discrete group. Fix an ergodic free nonsingular action of $\Gamma$ on a nonatomic standard probability space. Let $G$ be a compactly generated locally compact second countable group such that the closure of the group of inner automorphisms of $G$ is compact in the natural topology. It is shown that there exists a {\it bounded} ergodic $G$-valued cocycle of $\Gamma$.

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Alexandre I. Danilenko. 2019-09-02. On the bounded cohomology for ergodic nonsingular actions of amenable groups. https://arxiv.org/abs/1909.00620

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