Topological generators for full groups of hyperfinite pmp equivalence relations

TL;DR

This paper proves that the full group of any aperiodic hyperfinite pmp equivalence relation can be generated by just two elements, using an elementary construction and classical theorems.

Contribution

It provides an explicit elementary proof and construction of two topological generators for these full groups, extending previous results.

Findings

Explicit construction of topological generators for irrational circle rotations

Application of Dye's theorem and Baire category argument to general case

Simplification of previous proofs for full group generators

Abstract

We give an elementary proof that there are two topological generators for the full group of every aperiodic hyperfinite probability measure preserving Borel equivalence relation. Our proof explicitly constructs topological generators for the orbit equivalence relation of the irrational rotation of the circle, and then appeals to Dye's theorem and a Baire category argument to conclude the general case.