Journal of Symplectic Geometry

Volume 10 (2012)

Number 2

A product formula for Gromov-Witten invariants

Pages: 247 – 324

DOI: http://dx.doi.org/10.4310/JSG.2012.v10.n2.a5

Author

Clément Hyvrier

Abstract

We establish a product formula for Gromov–Witten invariants for closed relatively semi-positive Hamiltonian fibrations, with connected fiber, and over any connected symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked points in the total space of the Hamiltonian fibration to the corresponding moduli space of pseudo-holomorphic maps with marked points in the base. We use this induced map to recover the product formula by means of integration. Finally, we give applications to c-splitting and symplectic uniruledness.

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