Solid angles, magnetic fields and Seifert hypersurfaces

Given a knot K in R^3 we define a function F that assigns to a point x away of K the solid angle of a surface spanned by K. This is closely related to a scalar magnetic potential of a field induced by the magnetic current on K. It turns out that F is locally a fibration near K and the inverse images of non-critical values are Seifert surfaces for K. This analytic construction can be carried through in higher dimensions giving an explicit analytic construction of a Seifert hypersurface for general codimension 2 embeddings. Joint project with S. Dangskul (Edinburgh).