A field theory for symplectic fibrations over surfaces

Lalonde, Francois¹

¹ Department of Mathematics and Statistics, University of Montreal, Montreal H3C 3J7, Quebec, Canada

Geometry & topology, Tome 8 (2004) no. 3, pp. 1189-1226.

Résumé

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.

Détail

DOI : 10.2140/gt.2004.8.1189

Keywords: symplectic fibration, field theory, quantum cohomology, Floer homology, Hofer's geometry, commutator length

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