6533b835fe1ef96bd129e929

RESEARCH PRODUCT

ApproximatingL 2-invariants by their finite-dimensional analogues

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LetX be a finite connectedCW-complex. Suppose that its fundamental group π is residually finite, i.e. there is a nested sequence ... ⊂ Г m + 1 ⊂ Г m ⊂ ... ⊂ π of in π normal subgroups of finite index whose intersection is trivial. Then we show that thep-thL 2-Betti number ofX is the limit of the sequenceb p(Xm)/[π:Г m ] whereb p(Xm) is the (ordinary)p-th Betti number of the finite covering ofX associated with Г m .