A Product Formula for Gromov-Witten Invariants

TL;DR

This paper proves a product formula for Gromov-Witten invariants in Hamiltonian fibrations, linking the invariants of the total space and base, with applications to symplectic properties.

Contribution

It establishes a new product formula for Gromov-Witten invariants in Hamiltonian fibrations and explores its implications for symplectic geometry.

Findings

Derived a product formula for Gromov-Witten invariants in Hamiltonian fibrations.

Showed the moduli space map is a locally trivial orbifold fibration.

Applied the formula to results on c-splitting and symplectic uniruledness.

Abstract

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.