Correlated Gromov-Witten invariants
Correlated Gromov-Witten invariants
We introduce a geometric refinement of Gromov-Witten invariants for $\mathbb P^1$-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore we prove a refinement of the degeneration formula keeping track of the correlation. Finally, combining certain invariance properties of the correlated invariant, a …