An elementary approach to sofic equivalence relations

TL;DR

This paper provides an elementary framework for understanding sofic equivalence relations, explores their permanence properties, and addresses a key question about their characterization via full groups for aperiodic relations.

Contribution

It offers a simplified approach to sofic equivalence relations and answers an open question regarding their characterization through full groups.

Findings

Elementary description of sofic equivalence relations

Permanence properties for soficity established

Answered a question on soficity via full groups for aperiodic relations

Abstract

We present an elementary description of sofic equivalence relations, as well as some permanence properties for soficity. We answer a question by Conley, Kechris and Tucker-Drob of determining soficity in terms of the full group for aperiodic relations.