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Hamiltonian Gromov-Witten invariants. (English) Zbl 1032.53079
The author introduces invariants of compact symplectic manifolds with semi-free Hamiltonian actions of \(S^1\). These invariants are obtained by studying the moduli space of solutions to a set of equations generalizing both the holomorphicity equation used in Gromov-Witten theory and the certain gauge theoretical vortex equations. In the definition of the Hamiltonian Gromov-Witten invariants the author uses the ideas coming from gauge theory and the ideas underlying the construction of Gromov-Witten invariants.

53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
53D20 Momentum maps; symplectic reduction
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