A topological model for Oersted-Amp�re's law

1973

A geometrical description of Oersted-Ampere'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-Ampere'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}