  In this paper we construct a Universal chain complex, counting zeros of
closed 1-forms on a manifold. The Universal complex is a refinement of the well
known Novikov complex; it relates the homotopy type of the manifold, after a
suitable noncommutative localization, with the numbers of zeros of different
indices which may have closed 1-forms within a given cohomology class. The Main
Theorem of the paper generalizes the result of a joint paper with A. Ranicki,
which treats the special case of closed 1-forms having integral cohomology
classes. The present paper also describes a number of new inequalities, giving
topological lower bounds on the number of zeroes of closed 1-forms. In
particular, such estimates are provided by the homology of flat line bundles
with monodromy described by complex numbers which are not Dirichlet units.
