Borel reductions of profinite actions of SL(n,Z)

Abstract

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank \emph{strictly increases} in complexity with the rank. Subsequently, Thomas proved that the complexity of the classification problems for $p$-local torsion-free abelian groups of fixed rank $n$ are \emph{pairwise incomparable} as $p$ varies. We prove that if $3\le m<n$ and $p,q$ are distinct primes, then the complexity of the classification problem for $p$-local torsion-free abelian groups of rank $m$ is again incomparable with that for $q$-local torsion-free abelian groups of rank $n$.

References in corpus (3)

• Outer automorphism groups of some ergodic equivalence relations
• The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism
• Cocycle Superrigidity for Profinite Actions of Property (T) Groups

Cited by in corpus (2)

• Rotation equivalence and cocycle superrigidity
• Ioana's superrigidity theorem and orbit equivalence relations