Floer homology for almost Hamiltonian isotopies

Seidel introduced a homomorphism from the fundamental group π₁(Ham(M)) of the group of Hamiltonian diffeomorphisms of certain compact symplectic manifolds (M, ω) to a quotient of the automorphism group Aut(HF*(M, ω)) of the Floer homology HF*(M, ω). We prove a rigidity property: If two Hamiltonian loops represent the same element in π₁ (Diff(M)), then the image under the Seidel homomorphism of their classes in π₁(Ham(M)) coincide. The proof consists in showing that Floer homology can be defined by using 'almost Hamiltonian' isotopies, i.e. isotopies that are homotopic relatively to endpoints to Hamiltonian isotopies.