Wreath-like products of groups and their von Neumann algebras I: W*-superrigidity

• 成果类型: Article
• 署名作者: Chifan, Ionut; Ioana, Adrian; Osin, Denis; Sun, Bin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.198.3.6
• 发表日期: 2023
• 页码: 1261-1303
• 关键词: ergodic equivalence relations; ii1 factors; malleable actions; strong rigidity; property-t; bernoulli actions; COHOMOLOGY; CLASSIFICATION; fillings; rings

摘要

We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group G in a natural family of wreath-like products with property (T) is W*-superrigid: the group von Neumann algebra L(G) remembers the isomorphism class of G. This allows us to provide the first examples (in fact, 2(N0) pairwise non-isomorphic examples) of W*-superrigid groups with property (T).