2014/05/25 by Bohui Chen, Chen, Bohui, Bai-Ling Wang +2
Mathematics · #53D45 #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D45
paper · pdf · doi:10.48550/arxiv.1405.6387
a few typo are corrected, 41 pages
openalex publication_date 2014/05/25 · arxiv created 2014/06/07 · arxiv updated 2014/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,ω) be a compact symplectic manifold with a Hamiltonian action of a compact Lie group G and μ: X→ \mathfrak g be its moment map. In this paper, we study the L2-moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends. We studied a circle-valued action functional whose gradient flow equation corresponds to the symplectic vortex equations on a cylinder S1× \mathbb R. Assume that 0 is a regular value of the moment map μ, we show that the functional is of Bott-Morse type and its critical points of the functional form twisted sectors of the symplectic reduction (the symplecitc orbifold [μ-1(0)/G]). We show that any gradient flow lines approaches its limit point exponentially fast. Fredholm theory and compactness property are then established for the L2-Moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends.