A field theory for symplectic fibrations over surfaces
arXiv:math/0309335 · doi:10.2140/gt.2004.8.1189
Abstract
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.
arXiv commentPublished by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper32.abs.html