5 papers
A paradoxical route from hyperbolic geometry to proper proximality
D. Osin, K. Toyosawa, Z. Yang
For every integer , we introduce a new combinatorial condition PP inspired by paradoxical decompositions of groups. As increases, the property PP weakens, and…
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…
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…
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 von Neumann subalgebra , we prove that the amalgamated free product $M_{1}\overline{*}_{B}…
Weak exactness and amalgamated free product of von Neumann algebras
Kai Toyosawa
We show that the amalgamated free product of weakly exact von Neumann algebras is weakly exact. This is done by using a universal property of Toeplitz-Pimsner algebras and a locall…