Journal of Symplectic Geometry
- J. Symplectic Geom.
- Volume 1, Number 3 (2002), 543-646.
The symplectic vortex equations and invariants of Hamiltonian group actions
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants are based on the symplectic vortex equations. Applications include an existence theorem for relative periodic orbits, a computation for circle actions on a complex vector space, and a theorem about the relaton between the invariants introduced here and the Seiberg-Witten invariants of a product of a Riemann surface with a two-sphere.
J. Symplectic Geom., Volume 1, Number 3 (2002), 543-646.
First available in Project Euclid: 13 August 2004
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Cieliebak, Kai; Gaio, A. Rita; Mundet i Riera, Ignasi; Salamon, Dietmar A. The symplectic vortex equations and invariants of Hamiltonian group actions. J. Symplectic Geom. 1 (2002), no. 3, 543--646. https://projecteuclid.org/euclid.jsg/1092403032