We define the notion of mixed Frobenius structure (MFS) which is a generalization of the structure of a Frobenius manifold. We construct an MFS on the cohomology of weak Fano toric surfaces and that of the three-dimensional projective space using local Gromov–Witten invariants. This is an analogue of the Frobenius manifold associated to the quantum cohomology in the local Calabi–Yau setting.
"Mixed Frobenius structure and the local A-model." Kyoto J. Math. 60 (3) 997 - 1032, September 2020. https://doi.org/10.1215/21562261-2019-0053