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We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative Seidel morphism.doi:10.2140/gt.2011.15.1617 fatcat:uklt2ucg6zbarngjogyq2jtemy