A Product Formula for Gromov-Witten Invariants

Details A Product Formula for Gromov-Witten Invariants A Product Formula for Gromov-Witten Invariants

2009-04-09

arxiv.org/abs/0904.1492v2

Mathematics

Symplectic Geometry

59 pages, no figure, changes in the presention, minor corrections, added proofs in the gluing section.

Scientific paper

We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any 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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