The Residually Nite View: Approximation
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The L2-Betti numbers are related to classical Betti numbers through approximation by the normalised Betti numbers of finite index subgroups/finite coverings. We explain the (spectral) proof of this approximation theorem and briefly discuss the relation with other (homological) gradient invariants. This residually finite view will be complemented by the dynamical view in Chap. 5 and the approximation theorems for lattices in Chap. 6.
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