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

I define higher versions of contact structures on manifolds as maximallynon-integrable distributions. I call them multicontact structures. Cartan distributions on jet spaces provide canonical examples. More generally, I define higher versions of pre-contact structures as distributions on manifolds whose characteristic symmetries span a constant dimensional distribution. Every distribution is almost everywhere, locally, a pre-multicontact structure. After showing that the standard symplectization of contact manifolds generalizes naturally to a (pre-)multisymplectization of (pre-) multicontact manifolds, I associate a canonical L-infinity algebra to any (pre-)multicontact structure. Such L-infinity algebra is a higher version of the Jacobi brackets on contact manifolds. Since every partial differential equation (PDE) can be geometrically understood as a manifold with a distribution, then there is a (contact invariant) L-infinity algebra attached to any PDE. Finally, I describe in local coordinates the L-infinity algebra associated with the Cartan distribution on jet spaces.