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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.133, no.4, pp.1223-1230, 2005 (SCI-Expanded)
In this work we define a relative version of the flux homomorphism, introduced by Calabi in 1969, for a symplectic manifold. We use it to study ( the universal cover of) the group of symplectomorphisms of a symplectic manifold leaving a Lagrangian submanifold invariant. We also show that some quotients of the universal covering of the group of symplectomorphisms are stable under symplectic reduction.