The Gromov–Witten determination conjecture for the canonical natural transformation

Let a Lefschetz fibration arise from an anticanonical Lefschetz pencil, and choose the bulk term specified by the corresponding theorem. The Fukaya category has a canonical natural transformation from its Serre functor to the identity, and fibrewise compactification deforms this transformation. Gromov–Witten determination conjecture. The deformation of the canonical natural transformation is determined by Gromov–Witten invariants of the compactified total space. This extends the expected relationship between natural transformations in Fukaya categories of Lefschetz fibrations and Gromov–Witten theory; the paper describes the precise formulation through a differential equation whose coefficients are such invariants.