On the definition of L2-Betti numbers of equivalence relations

TL;DR

This paper demonstrates that the L2-Betti numbers of equivalence relations, as defined by Sauer and Gaboriau, are equivalent, unifying two approaches in the field.

Contribution

It establishes the equivalence of L2-Betti number definitions for equivalence relations by Sauer and Gaboriau, clarifying their relationship.

Findings

L2-Betti numbers of equivalence relations are consistent across definitions

Unification of two major approaches in the field

Provides a foundation for further research in the area

Abstract

We show that the L2-Betti numbers of equivalence relations defined by R. Sauer coincide with those defined by D. Gaboriau.