{"paper":{"title":"On the Superrigidity of Malleable Actions with Spectral Gap","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Sorin Popa","submitted_at":"2006-08-16T20:04:51Z","abstract_excerpt":"We prove that if a countable group $\\Gamma$ contains infinite commuting subgroups $H, H'\\subset \\Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\\Gamma$, then any measure preserving $\\Gamma$-action on a probability space which satisfies certain malleability, spectral gap and weak mixing conditions (e.g. a Bernoulli $\\Gamma$-action) is cocycle superrigid. If in addition $H'$ can be taken non-virtually abelian and $\\Gamma \\curvearrowright X$ is an arbitrary free ergodic action while $\\Lambda \\curvearrowright Y=\\Bbb T^\\Lambda$ is a Bernoulli action of an arbitrary infinite conjugacy c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608429","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/0608429/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"}