  In the first part of this paper we revisit a classical topological theorem by
Tischler (1970) and deduce a topological result about compact manifolds
admitting a set of independent closed forms proving that the manifold is a
fibration over a torus. As an application we reprove the Liouville theorem for
integrable systems asserting that the invariant sets or compact connected
fibers of a regular integrable system are tori. We give a new proof of this
theorem (including the non-commutative version) for symplectic and more
generally Poisson manifolds.
