Abstract. By using the cotangent bundle of a foliation and the foliated cohomology we extend some results concerning the flux homomorphism. In analogy to symplectomorphisms one defines the flux for the automorphism group of a regular Poisson manifold. Next the flux extends to the case of `foliated' loops. In view of the perfectness theorem the transgression homomorphism is an obstacle to further extension.
AMSclassification. Primary 58D05; Secondary 22E65
Keywords. Foliation, diffeomorphism group, foliated cohomology, flux homomorphism