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December, 2002 The symplectic vortex equations and invariants of Hamiltonian group actions
Kai Cieliebak , A. Rita Gaio , Ignasi Mundet i Riera , Dietmar A. Salamon
J. Symplectic Geom. 1(3): 543-646 (December, 2002).

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.

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Kai Cieliebak . A. Rita Gaio . Ignasi Mundet i Riera . Dietmar A. Salamon . "The symplectic vortex equations and invariants of Hamiltonian group actions." J. Symplectic Geom. 1 (3) 543 - 646, December, 2002.

Information

Published: December, 2002
First available in Project Euclid: 13 August 2004

zbMATH: 1093.53093
MathSciNet: MR1959059

Rights: Copyright © 2002 International Press of Boston

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Vol.1 • No. 3 • December, 2002
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