Approximating the first $L^2$-betti number of residually finite groups

Abstract

We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an application we construct a finitely generated infinite residually finite torsion group with positive first $L^2$-betti number.

References in corpus (2)

• Detecting large groups
• Applications of p-deficiency and p-largeness