Journal of Symplectic Geometry

The symplectic vortex equations and invariants of Hamiltonian group actions

Kai Cieliebak , A. Rita Gaio , Ignasi Mundet i Riera , and Dietmar A. Salamon

Abstract

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.

Article information

Source
J. Symplectic Geom., Volume 1, Number 3 (2002), 543-646.

Dates
First available in Project Euclid: 13 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1092403032

Mathematical Reviews number (MathSciNet)
MR1959059

Zentralblatt MATH identifier
1093.53093

Citation

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


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