L(2)-TOPOLOGICAL INVARIANTS OF 3-MANIFOLDS

We give results on the L(2)-Betti numbers and Novikov-Shubin invariant s of compact manifolds, especially 3-manifolds. We first study the Bet ti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequ ence of chain complexes, Our algebraic results, along with some analyt ic results on geometric 3-manifolds, are used to compute the L(2)-Bett i numbers of compact 3-manifolds which satisfy a weak form of the geom etrization conjecture, and to compute or estimate their Novikov-Shubin invariants.