Journal of Symplectic Geometry

Gromov--Witten invariants of symplectic quotients and adiabatic limits

Ana Rita Pires Gaio and Dietmar A. Salamon

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We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions to the symplectic vortex equations. Our main theorem asserts that the genus zero invariants of Hamiltonian group actions defined by these equations are related to the genus zero Gromov--Witten invariants of the symplectic quotient (in the monotone case) via a natural ring homomorphism from the equivariant cohomology of the ambient space to the quantum cohomology of the quotient.

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J. Symplectic Geom., Volume 3, Number 1 (2005), 55-159.

First available in Project Euclid: 13 April 2006

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Gaio, Ana Rita Pires; Salamon, Dietmar A. Gromov--Witten invariants of symplectic quotients and adiabatic limits. J. Symplectic Geom. 3 (2005), no. 1, 55--159.

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