Journal of Symplectic Geometry

Volume 1 (2001)

Number 3

The symplectic vortex equations and invariants of Hamiltonian group actions

Pages: 543 – 646

DOI: http://dx.doi.org/10.4310/JSG.2001.v1.n3.a3

Authors

Kai Cieliebak

A. Rita Gaio

Ignasi Mundet i Riera

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.

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