Hamiltonian Gromov–Witten invariants

In this paper we introduce invariants of semi-free Hamiltonian actions of S1 on compact symplectic manifolds using the space of solutions to certain gauge theoretical equations. These equations generalise both 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.