{"paper":{"title":"Cocycle and Orbit Equivalence Superrigidity for Malleable Actions of w-Rigid Groups","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Sorin Popa","submitted_at":"2005-12-30T08:45:37Z","abstract_excerpt":"We prove that if a countable discrete group $\\Gamma$ is {\\it w-rigid}, i.e. it contains an infinite normal subgroup $H$ with the relative property (T) (e.g. $\\Gamma= SL(2,\\Bbb Z) \\ltimes \\Bbb Z^2$, or $\\Gamma = H \\times H'$ with $H$ an infinite Kazhdan group and $H'$ arbitrary), and $\\Cal V$ is a closed subgroup of the group of unitaries of a finite von Neumann algebra (e.g. $\\Cal V$ countable discrete, or separable compact), then any $\\Cal V$-valued measurable cocycle for a measure preserving action $\\Gamma \\curvearrowright X$ of $\\Gamma$ on a probability space $(X,\\mu)$ which is weak mixing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512646","kind":"arxiv","version":8},"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/0512646/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"}