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Gromov-Witten invariants and quantization of quadratic Hamiltonians. (English) Zbl 1008.53072

The author describes a formalism based on quantization of quadratic Hamiltonians and symplectic actions of loop groups which provides a convenient home for most of the known results and conjectures about Gromov-Witten invariants of compact symplectic manifolds.

MSC:

53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
53D55 Deformation quantization, star products
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