Finitely presented simple groups and measure equivalence

Abstract

We exhibit explicit infinite families of finitely presented, Kazhdan, simple groups that are pairwise not measure equivalent. These groups are lattices acting on products of buildings. We obtain the result by studying vanishing and non-vanishing of their $L^2$-Betti numbers.

17 pages. Changes in version 2: proofs are formulated in a more clear way using nerves and some minor typos were corrected

References in corpus (1)

• Finite presentability of Kac-Moody groups over finite fields