Homological Lagrangian monodromy

Abstract

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.

17 pages; R. Leclercq joined as co-author and a second, more algebraic proof of the main result is added, and added references as well as comments.