English

A continuum of non-measure equivalent groups

Group Theory 2025-12-05 v1 Dynamical Systems Operator Algebras

Abstract

We construct a continuum sized family {Gx}x{0,1}N\{G_x\}_{x\in\{0,1\}^{\mathbb N}} of pairwise non-measure equivalent countable groups which have property (T) (hence are finitely generated), have zero 2\ell^2-Betti numbers of all orders, and are torsion-free.

Keywords

Cite

@article{arxiv.2512.04531,
  title  = {A continuum of non-measure equivalent groups},
  author = {Adrian Ioana and Robin Tucker-Drob},
  journal= {arXiv preprint arXiv:2512.04531},
  year   = {2025}
}
R2 v1 2026-07-01T08:09:00.349Z