Coamenability and strong ergodicity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910232564727808 |
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| author | Hayes, Ben |
| author_facet | Hayes, Ben |
| contents | 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 $Λ\leq Γ$ is a coamenable inclusion of groups, then any strongly ergodic $Γ$ action has countably many ergodic components for the $Λ$ action, each of which is strongly ergodic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18433 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coamenability and strong ergodicity Hayes, Ben Dynamical Systems Group Theory Operator Algebras 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 $Λ\leq Γ$ is a coamenable inclusion of groups, then any strongly ergodic $Γ$ action has countably many ergodic components for the $Λ$ action, each of which is strongly ergodic. |
| title | Coamenability and strong ergodicity |
| topic | Dynamical Systems Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2605.18433 |