On the bounded cohomology for ergodic nonsingular actions of amenable groups
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 $\Gamma$.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.00620
- arXiv:
- arXiv:1909.00620
- Bibcode:
- 2019arXiv190900620D
- Keywords:
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- Mathematics - Dynamical Systems;
- 37A40