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The more important difference between Riemann and pseudo-Riemann manifolds isthe metric signature and its theoretical consequences. The practicalapplication for Physics Theories becomes often impossible due to the signatureconsequences. Eg., some of the rich results in Riemann Geometry and Topologybecome invalid for Physics if they are based on the concept of the positivedefinite norm; to avoid this problem, the proof machinery must avoid suchassumption and must be based in other tools. This paper is a contribution toprovide methodologies for Hodge decomposition and \poincare duality based onthe concept of linear independence of canonical classes instead of the positivenorm.  As a result, the Hodge and norm decompositions are expressed based oncontinuous and discrete terms. When this result is applied to ClassicalElectromagnetic Theory, in pseudo-Riemann manifolds with minkowskian metric,magnitudes as the field norm and action have one discrete sum of terms. Thisresult, as a quantization of the norm and action is a property of the Topology,in special of the Cohomology classes, that are sources of the field as well asthe generators of action quantum.

The Poincare Duality in Quantization of the Norm of Differential Forms