Lagrangian Floer theory and mirror symmetry on compact toric manifolds
Symplectic Geometry
2016-03-25 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1009.1648,
title = {Lagrangian Floer theory and mirror symmetry on compact toric manifolds},
author = {Kenji Fukaya and Yong-Geun Oh and Hiroshi Ohta and Kaoru Ono},
journal= {arXiv preprint arXiv:1009.1648},
year = {2016}
}
Comments
292 pages, 23 figures; final version in Asterisque, vol 376, 2016, Societe Mathematique de France