{"paper":{"title":"Some computations of 1-cohomology groups and construction of non orbit equivalent actions","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Sorin Popa","submitted_at":"2004-07-12T17:51:54Z","abstract_excerpt":"For each group $G$ having an infinite normal subgroup with the relative property (T) (for instance $G = H \\times K$ where $H$ is infinite with property (T) and $K$ is arbitrary), and any countable abelian group $\\Lambda$ we construct free ergodic measure preserving actions $\\sigma_\\Lambda$ of $G$ on the probability space such that the 1'st cohomology group of $\\sigma_\\Lambda$, $H^1(\\sigma_\\Lambda)$, is equal to Char$(G) \\times \\Lambda$. We deduce that $G$ has uncountably many non stably orbit equivalent actions. We also calculate 1-cohomology groups and show existence of ``many'' non stably or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407199","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0407199/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}