Lagrangian Floer theory and mirror symmetry on compact toric manifolds

Details Lagrangian Floer theory and mirror symmetry on compact toric manifolds Lagrangian Floer theory and mirror symmetry on compact toric manifolds

2010-09-08

arxiv.org/abs/1009.1648v1

Mathematics

Symplectic Geometry

231 pages, 20 figures

Scientific paper

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.

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