Year: 2026
Type: preprint
Abstract: In this paper, we confirm a conjecture of Ozawa and others asserting that every finitely generated, relatively hyperbolic, exact group is bi-exact (in the sense of Ozawa) relative to its natural peripheral structure. As a consequence, every such group gives rise to a prime group von Neumann algebra. As an application, we construct a continuum family of property (T), relatively hyperbolic groups $\{G_i\}_{i\in I}$ such that, for every fixed arbitrary free, ergodic, probability measure-preserving action $G_i \curvearrowright Z_i$, the collection of associated group measure space von Neumann algebras $\{L^\infty(Z_i)\rtimes G_i\}_{i\in I}$ are pairwise non-stably $\ast$-isomorphic.
Source: arXiv (Cornell University)
Authors: Chifan, Ionuţ, Toyosawa, Kai, Yang, Zhiyuan
Institution: University of Iowa
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204241499
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