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

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

2010-11-22

arxiv.org/abs/1011.4739v2

Mathematics

Group Theory

Scientific paper

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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