  The axioms of topological electromagnetism are refined by the introduction of
the de Rham homology of k-vector fields on orientable manifolds and the use of
Poincare duality in place of Hodge duality. The central problem of defining the
electromagnetic constitutive law is elaborated upon in the linear and nonlinear
cases. The manner by which the spacetime metric might follow from the
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 the constitutive law is explored. The manner by which
wave motion might follow from the electromagnetic structure is also discussed.
