Coamenability and strong ergodicity

Ben Hayes

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arXiv · 2605.18433

Coamenability and strong ergodicity

Ben Hayes

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Abstract

Following methods of Bannon-Marrakchi-Ozawa, we show that for coamenable inclusion $\mathcal{S}\leq \mathcal{R}$ of ergodic, probability measure-preserving relations, we have that $\mathcal{R}$ is strongly ergodic if and only if $\mathcal{S}$ is strongly ergodic. More general results are given when $\mathcal{S}\leq \mathcal{R}$ is coamenable, $\mathcal{R}$ is strongly ergodic, but we do not assume ergodicity of $\mathcal{S}$. As a consequence, if $\Lambda\leq \Gamma$ is a coamenable inclusion of groups, then any strongly ergodic $\Gamma$ action has countably many ergodic components for the $\Lambda$ action, each of which is strongly ergodic.

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BibTeX RIS

Ben Hayes. 2026-05-18. Coamenability and strong ergodicity. https://arxiv.org/abs/2605.18433

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