The symplectic vortex equations and invariants of Hamiltonian group actions

By Kai Cieliebak, A. Rita Gaio, I. M. I. Riera, Dietmar Salamon. 2001

141 citations recorded by the source corpus.

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 relation between the invariants introduced here and the Seiberg– Witten invariants of a product of a Riemann surface with a two-sphere.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/09118eaa56c7092f2f8b835364e1ac512972db2e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stable quasimaps to GIT quotients (2011, methodology): “A sophisticated study of stacks of the type Mg,k([W/G], β) was begun in [14], with the goal to produce an algebro-geometric version of the “Gromov-Witten gauge invariants” introduced in symplectic geometry via solutions to vortex equations (see [7, 6, 38, 39, 17, 18]).”
Gauged Floer Theory Of Toric Moment Fibers (2010, background): “1”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, background): “…earlier constructed a Grothendieck-style compactification in the case that the target is a smooth projective variety, while in the symplectic setting Mundet [37] and Ott [39] show that the connected components of the moduli spaces of semistable gauged maps have a Kontsevich-style compactification.”