A long exact sequence for symplectic Floer cohomology

Let (M, ω, α) be a compact symplectic manifold with contact type boundary: α is a contact one-form on ∂M which satisfies dα = ω|∂M and makes ∂M convex. Assume in addition that [ω, α] ∈ H(M,∂M ;R) is zero, so that α can be extended to a one-form θ on M satisfying dθ = ω. After fixing such a θ once and for all, one can talk about exact Lagrangian submanifolds in M . The Floer cohomology of two such submanifolds is comparatively easy to define, since the corresponding action functional has no periods, so that bubbling is impossible. The aim of this paper is to prove the following result, which was announced in [25] (with an additional assumption on c1(M) that has been removed in the meantime).