{"paper":{"title":"The Borel complexity of von Neumann equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.LO","math.OA"],"primary_cat":"math.DS","authors_text":"Asger Tornquist, Inessa Epstein","submitted_at":"2011-09-11T20:34:21Z","abstract_excerpt":"We prove that for a countable discrete group $\\Gamma$ containing a copy of the free group $\\F_n$, for some $2\\leq n\\leq\\infty$, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free actions of $\\Gamma$ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving $\\Gamma$ actions. As a consequence we obtain that the isomorphism relation in the spaces of separably acting factors of type $\\II_1$, $\\II_\\infty$ and $\\III_\\lambda$, $0\\leq\\lambda\\leq 1$, are analytic and not Borel when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2351","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"}