Morse theory for Lagrangian intersections

Let P be a compact symplectic manifold and let L C P be a Lagrangian submanifold with 2{P,L) = 0. For any exact diffeomorphism of P with the property that (L) intersects L transverally, we prove a Morse inequality relating the set (L) L to the cohomology of L. As a consequence, we prove a special case of the Arnold conjecture: If r 2 (P) = 0 and is an exact diffeomorphism all of whose fixed points are nondegenerate, then the number of fixed points is greater than or equal to the sum over the Z2-Betti numbers of P.