A topological model for Oersted-Ampère's law

Abstract

A geometrical description of Oersted-Ampére's law ∮H ds=(4π/c)I can be given in terms of an appropriate topological manifold. More precisely: It will be shown that Oersted-Ampère's law can be related to the topological invariantH ¹(S ¹), i.e. de Rham's first cohomology group on the differentiable manifoldS ¹={(x,y) ∈ ℝ²∶x ²+y ²}