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Mathematics > Symplectic Geometry

arXiv:math/0002121 (math)
[Submitted on 15 Feb 2000]

Title:Hamiltonian Gromov-Witten invariants

Authors:Ignasi Mundet i Riera
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Abstract: In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical equations. These equations generalize at the same time the vortex equations and the holomorphicity equation used in Gromov-Witten theory. In the definition of the invariants we combine ideas coming from gauge theory and the ideas underlying the construction of Gromov-Witten invariants. This paper is based on a part of my PhD Thesis (see math/9912150).
Comments: 36 pages
Subjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG); Differential Geometry (math.DG)
MSC classes: 53D45; 53C07
Cite as: arXiv:math/0002121 [math.SG]
  (or arXiv:math/0002121v1 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.math/0002121

Submission history

From: Ignasi Mundet i Riera [view email]
[v1] Tue, 15 Feb 2000 14:26:10 UTC (38 KB)
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