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2004 A field theory for symplectic fibrations over surfaces
Francois Lalonde
Geom. Topol. 8(3): 1189-1226 (2004). 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.

Citation

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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

Information

Received: 20 September 2003; Revised: 22 August 2004; Accepted: 11 July 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1078.53091
MathSciNet: MR2087081
Digital Object Identifier: 10.2140/gt.2004.8.1189

Subjects:
Primary: 53D45
Secondary: 37J50, 53D40, 81T40

Rights: Copyright © 2004 Mathematical Sciences Publishers

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Vol.8 • No. 3 • 2004
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