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We introduce a contravariant functor, called Floer functor, from the categoryof Lagrangian conductors of a symplectic manifold to the homotopy category ofbounded chain complexes of open strings in this manifold. The latter twocategories are defined for all symplectic manifolds, whereas Floer functor isdefined for semipositive manifolds which are either closed or convex atinfinity. We then prove that when the first Chern class of the symplecticmanifold vanishes, Lagrangian spheres define Lagrangian conductors so that inparticular their integral Floer cohomology is well defined. This requires theintroduction of singular almost-complex structures given by symplectic fieldtheory.

Open strings, Lagrangian conductors and Floer functor