In this talk we introduce a geometric refinement of Gromov-Witten invariants for P1-bundles relative to the natural fiberwise boundary structure. We call these refined invariants correlated Gromov-Witten invariants. We will introduce the correlated invariants, discuss their properties and provide some computations in the case of P1-bundles over an elliptic curve. Such invariants are expected to play a role in the degeneration formula for reduced Gromov-Witten invariants for abelian and K3 surfaces. This is a joint work with Thomas Blomme.