Novikov - Shubin signatures, II

Abstract

This paper continues math.DG/9903140. Here we construct a linking form on the torsion part of middle dimensional extended L^2 homology and cohomology of odd-dimensional manifolds. We give a geometric necessary condition when this linking form is hyperbolic. We compute this linking form in case when the manifold bounds. We introduce and study new numerical invariants of the linking form: the Novikov - Shubin signature and the torsion signature. We compute these invariants explicitly for manifolds with $\pi_1 = Z$ in terms of the Blanchfield form. We develop a notion of excess for extensions of torsion modules and show how this concept can be used to guarantee vanishing of the torsion signature.