The class of coisotropic submanifolds of symplectic manifolds encompasses Lagrangians and hypersurfaces, which makes them very general, interesting and hard to study. In the first part of my talk I will introduce coisotropics and explain how they are present in many areas of geometry and physics: they feature prominently in “the general Hamiltonian theory” (Dirac) and provide a starting point for quantum mechanics and Poisson geometry. Symplectic group actions, foliations and certain dynamical systems can all be viewed from a coisotropic perspective.
In the second part of my talk I will focus on a special class of fibered coisotropics and explain how we obtain restrictions on the topology of the base of the fibration by analysing the Floer complex associated to the coisotropic and neck stretching techniques from symplectic field theory.