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Keywords:

  • Topological electromagnetism;
  • de Rham homology;
  • electromagnetic constitutive laws;
  • intersection form;
  • wave structures on manifolds

Abstract

The axioms of topological electromagnetism that were given by Hehl, Obukhov, and Rubilar are refined by the use of geometrical and topological notions that are found on orientable manifolds. The central problem of defining the spacetime electromagnetic constitutive law in terms of the geometrical and topological structure of the spacetime manifold is elaborated upon in the linear and nonlinear cases. The manner by which the spacetime metric might follow from the electromagnetic constitutive law is examined in the linear case. The possibility that the intersection form of the spacetime manifold might play a role in defining a topological basis for a nonlinear electromagnetic constitutive law is explored. The manner by which electromagnetic wave motion relates to the geometric structure is also discussed.