Geometry & Topology, Vol. 8 (2004)
Paper no. 32, pages 1189--1226.
A field theory for symplectic fibrations over surfaces
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
Symplectic fibration, field theory, quantum cohomology, Floer homology, Hofer's geometry, commutator length
AMS subject classification.
Secondary: 53D40, 81T40, 37J50.
Submitted to GT on 20 September 2003.
(Revised 22 August 2004.)
Paper accepted 11 July 2004.
Paper published 10 September 2004.
Notes on file formats
Department of Mathematics and Statistics, University of Montreal
Montreal H3C 3J7, Quebec, Canada
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