Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I will present an approach to the concept of a contact manifold which, in contrast to the one dominating in the physics literature, serves also for non-trivial contact structures. In this approach contact geometry is not an ‘odd-dimensional cousin’ of symplectic geometry, but rather a part of the latter, namely ‘homogeneous symplectic geometry’. This understanding of contact structures is much simpler than the traditional one and very effective in applications, reducing, for instance, the contact Hamiltonian formalism to the standard symplectic picture.