Finite dimensional approximations for the symplectic vortex equations

2004/08/09 by Urs Frauenfelder, Frauenfelder, Urs
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.math/0408102

28 pages

arxiv created 2004/08/09 · openalex publication_date 2004/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Furuta's finite dimensional approximations for the flow lines of the Moment action functional for toric symplectic orbifolds and show their relation to Givental's toric map space.

Citations

• Quantum Cohomology and Morse Theory on the Loop Space of Toric Varieties
• Yang-Mills-Higgs theory for symplectic fibrations
• The Arnold-Givental conjecture and moment Floer homology

Related

• Symplectic structures and dynamics on vortex membranes
• Vortex invariants and toric manifolds
• The symplectic vortex equations and invariants of Hamiltonian group actions
• L²-moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends
• The Asymptotic Behavior of Finite Energy Symplectic Vortices with Admissible Metrics