Finitely presented simple groups and measure equivalence
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 261-279
MSC: Primary 20E32; Secondary 20E42, 20F05, 20F55, 20J05, 20J06, 22E41, 28D15.
DOI: 10.4064/cm8610-11-2022
Published online: 13 February 2023
Abstract
We exhibit explicit infinite families of finitely presented, Kazhdan, simple groups that are pairwise non-measure-equivalent. These groups are lattices acting on products of buildings. We obtain the result by studying vanishing and non-vanishing of their $\ell ^2$-Betti numbers.
