Gromov-Witten type invariants on circle bundles over symplectic manifolds

Abstract

We consider circle bundles over symplectic manifolds to study Gromov-Witten type invariants. We investigate the moduli space of pseudo-coholomorphic maps, Gromov-Witten type invariant, the quantum type cohomology of the total space which has a natural contact structure. We then compare Gromov-Witten invariant, and quantum cohomology of the base space with the one of the total space, and derive some relations between them.