{"paper":{"title":"Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Cyril Houdayer, Yusuke Isono","submitted_at":"2015-10-27T17:02:19Z","abstract_excerpt":"We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras $M = B \\rtimes \\Gamma$ arising from arbitrary actions $\\Gamma \\curvearrowright B$ of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra $N' \\cap M^\\omega$ of any nonamenable von Neumann subalgebra with normal expectation $N \\subset M$. We use this result to show that for any strongly ergodic essentially free nonsingular action $\\Gamma \\curvearrowright (X, \\mu)$ of any bi-exact countable discrete g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07987","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"}