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.
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