Hamiltonian Gromov-Witten invariants

2000/02/15 by Ignasi Mundet i Riera, Riera, Ignasi Mundet i · 1 citation
Mathematics · #53C07 #53D45 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.DG #math.SG #msc:53C07 #msc:53D45

paper · pdf · doi:10.48550/arxiv.math/0002121

36 pages

arxiv created 2000/02/15 · openalex publication_date 2000/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

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