We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and Floer homologies that are canonically attached to the fibration. We prove a composition theorem in the spirit of QFT, and show that this field theory applie...

1.1. Stable propagation. Let M := UT be the open unit cotangent bundle of the n-dimensional Euclidean torus T = R/Z. We express the elements of M in terms of the canonical coordinates (q1, . . . , qn, p1, . . . , pn), where qi ≡ qi + 1. Thus we identify M with T × D, where D = {|p| < 1} is the open unit ball in R and |v| stands for the Euclidean norm of a vector v ∈ R. Consider the space H of a...

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