L2-torsion, the measure-theoretic determinant conjecture, and uniform measure equivalence

TL;DR

This paper establishes that L2-torsion remains invariant under uniform measure equivalence for groups satisfying a measure-theoretic determinant conjecture, which is verified for certain Bernoulli actions.

Contribution

It introduces a measure-theoretic version of the determinant conjecture and proves its validity for Bernoulli actions of residually amenable groups, linking it to L2-torsion invariance.

Findings

L2-torsion is invariant under uniform measure equivalence given the measure-theoretic determinant conjecture.

The measure-theoretic determinant conjecture is verified for Bernoulli actions of residually amenable groups.

The paper connects measure-theoretic properties with algebraic invariants like L2-torsion.

Abstract

We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for instance, proved for Bernoulli actions of residually amenable groups.