{"paper":{"title":"An Uncountable Family of Non Orbit Equivalent Actions of $\\Bbb F_n$","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Damien Gaboriau, Sorin Popa","submitted_at":"2003-05-31T18:22:40Z","abstract_excerpt":"For each $2 \\leq n \\leq \\infty$, we construct an uncountable family of free ergodic measure preserving actions $\\alpha_t$ of the free group $\\Bbb F_n$ on the standard probability space $(X, \\mu)$ such that any two are non orbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid'' (in the sense of [Po01]), with the II$_1$ factors $L^\\infty(X, \\mu)\\rtimes_{\\alpha_t} \\Bbb F_n$ mutually non stably isomorphic (even non-stably isomorphic) and in the class $\\Cal H\\Cal T_{_{s}}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306011","kind":"arxiv","version":4},"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/0306011/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"}