Cotangent paths as coisotropic subsets for local functions

Overview & Synopsis

We establish a local function version of a classical result claiming that a bivector field on a manifold M is Poisson if and only if cotan-gent paths form a coisotropic set of the infinite dimensional symplectic manifold of paths valued in T * M. Our purpose here is to prove this result without using the Banach manifold setting, setting which fails in the periodic case because cotangent loops do not form a Banach sub-manifold. Instead, we use local functions on the path space, a point of view that allows to speak of a coisotropic set.