  To a pair (X,f), X compact ANR and f a continuous angle valued map defined on
X, a fixed field and a nonnegative integer one assigns a finite configuration
of complex numbers with multiplicities located in the punctured complex plane
and a finite configuration of free modules over the ring of Laurent polynomials
(with coefficients in the fixed field) indexed by the same complex numbers.
This is done in analogy with the configuration of eigenvalues and of
generalized eigenspaces of an invertible linear operator in a finite
dimensional complex vector space. The configuration of complex numbers refines
the Novikov - Betti number and the configuration of free modules refines the
Novikov homology associated with the cohomology class defined by f, in the same
way the collection of eigenvalues and of generalized eigen-spaces refine the
dimension of the vector space and the vector space on which the operator acts.
  In the case the field is the field of complex numbers the configuration of
free modules induces by "von-Neumann completion" a configuration of mutually
orthogonal closed Hilbert submodules of the L 2--homology of the infinite
cyclic cover of X determined by the map f, which is an Hilbert module over the
von-Neumann algebra of complex L-infinity functions on the unit circle in the
complex plane.
