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Symplectic fibrations and the abelian vortex equations

T. Perutz
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Abstract

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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T. Perutz. 2007-08-10. Symplectic fibrations and the abelian vortex equations. https://arxiv.org/abs/math/0606063

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