Symplectic fibrations and the Abelian vortex equations
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Publication:930570
DOI10.1007/S00220-007-0402-4zbMATH Open1152.53067arXivmath/0606063OpenAlexW2078980317MaRDI QIDQ930570
Author name not available (Why is that?)
Publication date: 1 July 2008
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/math/0606063
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