Non-amenable principal groupoids with weak containment

TL;DR

This paper constructs examples of principal groupoids that exhibit weak containment without being amenable, addressing open questions in the theory of groupoids and operator algebras.

Contribution

It provides the first known examples of non-amenable principal groupoids with weak containment, resolving longstanding open questions.

Findings

Existence of principal groupoids with weak containment but non-amenability

Counterexamples to the assumption that weak containment implies amenability

Advancement in understanding the structure of groupoids and their operator algebras

Abstract

We construct examples of principal groupoids that have weak containment but are not amenable, thus answering questions by Claire Anantharaman-Delaroche and Rufus Willett.