Symplectic Geometry Seminar

Consider a contact three-manifold, and within it a symplectic surface with boundary on Reeb orbits. We show that assuming a certain inequality on the rotation numbers of the boundary Reeb orbits, there must exist Reeb orbits which intersect the interior of the surface. Moreover, we obtain such orbits with an explicit lower bound on the “frequency” of these intersections (the number of intersections divided by symplectic action).  Applying this result to the special case of a global surface of section leads to a generalization of various recent results relating the mean action to the Calabi invariant for area-preserving surface diffeomorphisms.