Invariants of contact structures and transversally oriented foliations

We exhibit new invariants of the contact structure E(alpha), the contact flow F-alpha and the transverse symplectic geometry of a contact manifold (M, alpha). The invariant of contact structures generalizes to transversally oriented foliations. We focus on the particular cases of orientations of smooth manifolds and transverse orientations of foliations. We define the transverse Calabi invariants and determine their kernels.