APPROXIMATING L(2)-INVARIANTS BY THEIR FINITE-DIMENSIONAL ANALOGS

Let X be a finite connected CW-complex. Suppose that its fundamental group pi is residually finite, i.e. there is a nested sequence ... subset-of GAMMA(m+1) subset-of GAMMA(m) subset-of ... C pi of in pi normal subgroups of finite index whose intersection is trivial. Then we show that the p-th L2-Betti number of X is the limit of the sequence b(p)(X(m))/[pi:GAMMA(m)] where b(p)(X(m)) is the (ordinary) p-th Betti number of the finite covering of X associated with GAMMA(m).