Lagrangian Floer theory and Mirror symmetry on compact toric manifolds

By K. Fukaya, Yong-Geun Oh, H. Ohta, K. Ôno. Astérisque, 2010

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In this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We 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 \cite{fooo09} via the Floer cohomology deformed by ambient cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ba300c5a1a55fe04c45a916c7d82ce5027abae8b