The Poincaré Lemma and Potentials
5.1. A More General Stokes’s Theorem
We shall accept the following technical generalizations of results already proven.
Let Vp be a compact oriented submanifold (perhaps with boundary) of Mn and let F : Mn → Wm be a smooth map into a manifold Wm. The image F(V) in W need not be a submanifold. It might have self-intersections and all sorts of pathologies. Still, if βp is a form on W, it makes sense to talk of the integral of β over F(V) and in fact
which generalizes (3.17). In a sense, ...