A field theory for symplectic fibrations over surfaces
نویسنده
چکیده
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 applies naturally to the problem of minimising geodesics in Hofer’s geometry. This work can be considered as a natural framework that incorporates both the Piunikhin–Salamon–Schwarz morphisms and the Seidel isomorphism. AMS Classification numbers Primary: 53D45 Secondary: 53D40, 81T40, 37J50
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