Journal of Symplectic Geometry

Volume 14 (2016)

Number 4

Absolute vs. relative Gromov–Witten invariants

Pages: 1189 – 1250



Mohammad F. Tehrani (Simons Center for Geometry and Physics, SUNY, Stony Brook, New York, U.S.A.)

Aleksey Zinger (Department of Mathematics, SUNY, Stony Brook, Stony Brook, New York, U.S.A.)


We compare the absolute and relative Gromov–Witten invariants of compact symplectic manifolds when the symplectic hypersurface contains no relevant holomorphic curves. We show that these invariants are then the same, except in a narrow range of dimensions of the target and genera of the domains, and provide examples when they fail to be the same.

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