Diffiety

A diffiety is the infinite-dimensional geometric object obtained by adjoining all differential consequences of a system of partial differential equations. More precisely, it is a profinite-dimensional manifold, meaning an inverse limit of finite-dimensional jet bundles, equipped with a finite-dimensional Cartan distribution. This is an involutive distribution: the Lie bracket of any two vector fields tangent to the distribution is again tangent to it. The Cartan distribution is locally modeled on the infinite prolongation of a differential equation. Its integral manifolds, whose tangent spaces equal the distribution along them, correspond to solutions of the original system. Diffieties provide a coordinate-independent setting for symmetries, conservation laws, and the geometry of differential equations.