  For a continuous angle-valued map defined on a compact ANR, a fixed field and
any degree one proposes a refinement of the Novikov-Betti number and of the
Novikov homology of the pair consisting of the ANR and the degree one integral
cohomology class represented by the map. For each degree the first refinement
is a configuration of points with multiplicity located in the punctured complex
plane whose total cardinality is the Novikov-Betti number of the pair. The
second refinement is a configuration of submodules of the Novikov homology
whose direct sum is isomorphic to the Novikov homology and which has the same
support as the first configuration. When the field is a the field of complex
numbers the second configuration is convertible into a configuration of
mutually orthogonal closed Hilbert submodules of the L2-homology of the
infinite cyclic cover of the ANR defined by the angle-valued map. One discusses
the properties of these configurations namely, robustness with respect to
continuous perturbation of the angle-valued map and the Poincar\'e Duality and
one derives some computational applications in topology. The main results
parallel the results for the case of real-valued map but with Novikov homology
and Novikov-Betti numbers replacing standard homology and standard Betti
numbers.
