Lagrangian Floer Theory and Mirror Symmetry on Compact Toric Manifolds

In this volume, the authors study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. They construct a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of the toric manifold and of Saito's theory of singularities of the potential function constructed in [Fukaya, Tohoku Math. J. 63 (2011)] via the Floer cohomology deformed by ambient cycles. Their proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop.