Classical electromagnetism is shown to be equivalent to a course topology defined on a set of independent variables in terms of two fundamental exterior differential systems. The domains of support for finite non-zero electromagnetic field intensities, and finite non-zero electromagnetic currents, in general cannot be compact without boundary. The only exceptions occur when the Euler characteristic of the compact domain is zero. On a domain of four independent variables, the course topology can induce two other exterior differential systems that lead to the independent concepts of topological torsion and topological spin. The exterior derivative of these two 3-forms define the Poincare deformation invariants of the electromagnetic system. The vanishing of the two 3-forms can be used to define the concepts of transverse magnetic and transverse electric modes on topological grounds. The four dimensional lines in space time associated with the 3-forms of topological torsion and topological spin can exhibit linking and separation into component domains. The possible evolution of these topological properties is studied with respect to classes of processes that can be defined in terms of singly parameterized vector fields. Non-zero values of the Poincare invariants are the source of topological and thermodynamic change.

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