Abstract

The universal cover of the group of all diffeomorphisms preserving a given contact structure admits a natural bi-invariant relation. The question whether this relation is a partial order has strong connections to the topological and dynamical properties of the underlying contact manifold, such as the existence of closed Reeb orbits, certain types of fixed points or symplectic fillings. In this talk we will discuss several examples of orderable and non-orderable contact manifolds. The talk is partially based on joint work with Dylan Cant and Eric Kilgore, as well as with Egor Shelukhin.