Relative Biexactness for Relative Hyperbolic Groups and Some Applications

Ionuţ Chifan; Kai Toyosawa; Zhiyuan Yang

doi:10.48550/arxiv.2608.23991

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Relative Biexactness for Relative Hyperbolic Groups and Some Applications

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Relative Biexactness for Relative Hyperbolic Groups and Some Applications

Ionuţ Chifan, Kai Toyosawa and Zhiyuan Yang

arXiv

08/25/2026

DOI: 10.48550/arxiv.2608.23991

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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{Gᵢ}_(i∈ I)such that, for every fixed arbitrary free, ergodic, probability measure-preserving actionGᵢ ↷ Zᵢ , the collection of associated group measure space von Neumann algebras{L^(∞)(Zᵢ)⋈ Gᵢ}_(i∈ I)are pairwise non-stably∗ -isomorphic.

Mathematics - Group Theory

Mathematics - Operator Algebras

Details

Title: Subtitle: Relative Biexactness for Relative Hyperbolic Groups and Some Applications
Creators: Ionuţ Chifan
Kai Toyosawa
Zhiyuan Yang
Resource Type: Preprint
Publication Details: arXiv
DOI: 10.48550/arxiv.2608.23991
ISSN: 2331-8422
Publisher: arXiv
Language: English
Date posted: 08/25/2026
Academic Unit: Mathematics
Record Identifier: 9985220286502771

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