Open Calabi–Yau mirror symmetry for cohomology F-manifolds

Let $M$ and $M^{\vee}$ be open Calabi–Yau manifolds that are mirror to each other in the sense of homological mirror symmetry. A ring isomorphism is an isomorphism preserving the products on the rings involved, and a cohomology F-manifold is the algebraic structure defined in the paper by the relevant cohomological vector field and tensor operations. Open Calabi–Yau mirror symmetry conjecture. The ring isomorphism

$$\operatorname{SH}^*(M)\cong\operatorname{H}^*(M^{\vee},\bigwedge^*T_{M^{\vee}})$$

can be lifted to an isomorphism of cohomology F-manifolds. This would extend classical closed Calabi–Yau mirror symmetry to the open setting, where the structures need not extend to Frobenius manifolds because the Lie bracket may be nonzero. The paper presents this as a conjectural generalization and does not establish it.