Journal of Symplectic Geometry

Gromov--Witten invariants of symplectic quotients and adiabatic limits

Ana Rita Pires Gaio and Dietmar A. Salamon

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 13 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1144947823

Mathematical Reviews number (MathSciNet)
MR2198773

Zentralblatt MATH identifier
1143.53080

Citation

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. https://projecteuclid.org/euclid.jsg/1144947823


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