The more important difference between Riemann and pseudo Riemann manifolds is
the metric signature and its theoretical consequences. The scientific
literature in Riemann manifolds is sound and extensive. However, the practical
application for Physics Theories becomes often impossible due to the signature
consequences. Eg., some of the rich results in Riemann Geometry and Topology
becomes invalid for Physics if they are based on the concept of positive semi
definite norm. To avoid this problem, the proof machinery must avoid such
assumption and must be based in other tools. This paper is a contribution to
provide methodologies for Hodge decomposition and \poincare duality based on
the concept of linear independence instead of positive norm.
As result, the Hodge decomposition and also the norm decomposition are
expressed based on continuous and discrete terms. When this results are applied
to Classical Electromagnetic Theory, in pseudo Riemann manifolds with
minkowskian metric, magnitudes as the field norm and action have one discrete
stepwise term. This result of quantization of the norm is a property of the
Topology, in special of the Cohomology classes.