Symplectic fibrations and the abelian vortex equations

Details Symplectic fibrations and the abelian vortex equations Symplectic fibrations and the abelian vortex equations

2006-06-02

arxiv.org/abs/math/0606063v2

Mathematics

Symplectic Geometry

19 pages; accepted for publication in Comm. Math. Phys. Revised version corrects typos and clarifies discussion of Floer homol

Scientific paper

The nth symmetric product of a Riemann surface carries a natural family of Kaehler forms, arising from its interpretation as a moduli space of abelian vortices. We give a new proof of a formula of Manton-Nasir for the cohomology classes of these forms. Further, we show how these ideas generalise to families of Riemann surfaces. These results help to clarify a conjecture of D. Salamon on the relationship between Seiberg-Witten theory on 3-manifolds fibred over the circle and symplectic Floer homology.

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