Classification results for nonsingular Bernoulli crossed products

TL;DR

This paper establishes rigidity and classification results for type III factors arising from nonsingular Bernoulli actions of free and free product groups, expanding understanding beyond probability measure preserving cases.

Contribution

It provides the first classification results for nonsingular Bernoulli crossed products of type III$_1$ factors beyond the probability measure preserving setting.

Findings

Identifies a large family of nonisomorphic Bernoulli crossed products of type III$_1$

Shows these cannot be distinguished by Connes τ-invariant

Extends classification theory to nonsingular actions

Abstract

We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $\tau$-invariant. These are the first such classification results beyond the well studied probability measure preserving case.