Symplectic fibrations and the abelian vortex equations
Symplectic Geometry
2011-11-09 v2
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.
Keywords
Cite
@article{arxiv.math/0606063,
title = {Symplectic fibrations and the abelian vortex equations},
author = {T. Perutz},
journal= {arXiv preprint arXiv:math/0606063},
year = {2011}
}
Comments
19 pages; accepted for publication in Comm. Math. Phys. Revised version corrects typos and clarifies discussion of Floer homology