Some topological and metric properties of the space of Lorentz metrics

The space of smooth foliated mappings is modeled on the space of foliated 1-forms to introduce a manifold structure. This enables to generalize a so-called Weinsteinʹs chart to the automorphism group of a regular Poisson manifold. The existence of the "Poisson" flux homomorphism leads to a characterization of Hamiltonian diffeomorphisms