{"paper":{"title":"Orbit equivalence, coinduced actions and free products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Lewis Bowen","submitted_at":"2009-06-24T22:08:50Z","abstract_excerpt":"The following result is proven. Let $G_1 \\cc^{T_1} (X_1,\\mu_1)$ and $G_2 \\cc^{T_2} (X_2,\\mu_2)$ be orbit-equivalent, essentially free, probability measure preserving actions of countable groups $G_1$ and $G_2$. Let $H$ be any countable group. For $i=1,2$, let $\\Gamma_i = G_i *H$ be the free product. Then the actions of $\\Gamma_1$ and $\\Gamma_2$ coinduced from $T_1$ and $T_2$ are orbit-equivalent. As an application, it is shown that if $\\Gamma$ is a free group, then all nontrivial Bernoulli shifts over $\\Gamma$ are orbit-equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4573","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}