A Frobenius theorem on convenient manifolds (Q5957814)

A locally convex topological vector space is said to be convenient provided it is \(C^\infty\)-complete. Frobenius theorems are necessary and sufficient conditions for \(n\)-dimensional subbundles of the tangent bundle of a manifold to be the tangent bundle of a foliation. In this paper, using the convenient calculus of \textit{A. Kriegl} and \textit{P. W. Michor} [`The convenient setting of global analysis' (Providence, American Mathematical Society) (1997; Zbl 0889.58001)], the author proves a Frobenius theorem for finite-dimensional involutive subbundles of the tangent bundle of a convenient manifold. Lie's second fundamental theorem and Nelson's theorem are provided as applications of this theorem in the convenient case.