A field theory for symplectic fibrations over surfaces
Symplectic Geometry
2014-11-11 v4 Differential Geometry
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.
Keywords
Cite
@article{arxiv.math/0309335,
title = {A field theory for symplectic fibrations over surfaces},
author = {Francois Lalonde},
journal= {arXiv preprint arXiv:math/0309335},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper32.abs.html