3 papers
math.OA2026
Properly proximal countable measured groupoids
Adriana Fernández Quero, Kai Toyosawa
We introduce the notion of proper proximality for countable measured groupoids, extending the corresponding notion for countable groups. We prove that this groupoid property is equ…
math.OA2026
Relative Biexactness for Relative Hyperbolic Groups and Some Applications
Ionuţ Chifan, Kai Toyosawa, Zhiyuan Yang
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…
math.OA2025
On Relative Biexactness of Amalgamated Free Product von Neumann Algebras
Kai Toyosawa, Zhiyuan Yang
Given weakly exact tracial von Neumann algebras with a common injective amalgam , we prove that the amalgamated free product is biexa…