A Product Formula for Gromov-Witten Invariants
Symplectic Geometry
2010-03-16 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.0904.1492,
title = {A Product Formula for Gromov-Witten Invariants},
author = {Clément Hyvrier},
journal= {arXiv preprint arXiv:0904.1492},
year = {2010}
}
Comments
59 pages, no figure, changes in the presention, minor corrections, added proofs in the gluing section.