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.
Citation
Francois Lalonde. "A field theory for symplectic fibrations over surfaces." Geom. Topol. 8 (3) 1189 - 1226, 2004. https://doi.org/10.2140/gt.2004.8.1189
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