Let M be a symplectic manifold and let \phi be a Hamiltonian diffeomorphism. During the last twenty years, symplectic topologists intensively studied the following two questions:
Consider now a coisotropic submanifold Q in M. A point x in Q is called a leaf-wise fixed point of \phi if x and \phi(x) lie in the same isotropic leaf of Q. Generalizing the above questions, one may ask if there is a lower bound on the number of leaf-wise fixed points of \phi. The main result of this talk is that under suitable assumptions on M, Q, and \phi, such a bound is given by the sum of the \Z_2-Betti numbers of Q.
- How many fixed points does \phi at least have?
- Given a Lagrangian submanifold L in M, how many intersection points do L and \phi(L) at least have?