2006/06/02 by Tim Perutz, T. Perutz, Perutz, T.
Mathematics · #53D30 #53D40 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.SG #msc:53D30 #msc:53D40
paper · pdf · doi:10.48550/arxiv.math/0606063
19 pages; accepted for publication in Comm. Math. Phys. Revised version corrects typos and clarifies discussion of Floer homology
openalex publication_date 2006/06/02 · arxiv created 2007/08/10 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.