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

W. Lück; D. Osin

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arXiv · 1011.4739

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

W. Lück·D. Osin

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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.

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W. Lück, D. Osin. 2010-11-22. Approximating the first $L^2$-betti number of residually finite groups. https://arxiv.org/abs/1011.4739

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