Abstract
For a transversal pair of closed Lagrangian submanifolds L,L′ of a symplectic manifold M such that π1(L)=π1(L′)=0=c1|π2(M)=ω|π2(M) and for a generic almost complex structure J, we construct an invariant with a high homotopical content which consists in the pages of order ≥2 of a spectral sequence whose differentials provide an algebraic measure of the high-dimensional moduli spaces of pseudo-holomorpic strips of finite energy that join L and L′. When L and L′ are Hamiltonian isotopic, we show that the pages of the spectral sequence coincide (up to a horizontal translation) with the terms of the Serre spectral sequence of the path-loop fibration ΩL→PL→L and we deduce some applications.

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