Localized mirror functor constructed from a Lagrangian torus

Cheol-Hyun Cho Seoul National University Hansol Hong Harvard University Siu-Cheong Lau Boston University

Differential Geometry mathscidoc:1610.10015

Journal of Geometry and Physics
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A∞-functor from the Fukaya category of X to the category of matrix factorizations of W. It provides a unified way to construct matrix factorizations from Lagrangian Floer theory. The technique is applied to toric Fano manifolds to transform Lagrangian branes to matrix factorizations. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space.
SYZ, mirror symmetry, functor, homological, matrix factorization
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  title={Localized mirror functor constructed from a Lagrangian torus},
  author={Cheol-Hyun Cho, Hansol Hong, and Siu-Cheong Lau},
  booktitle={Journal of Geometry and Physics},
Cheol-Hyun Cho, Hansol Hong, and Siu-Cheong Lau. Localized mirror functor constructed from a Lagrangian torus. In Journal of Geometry and Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161004023752999851080.
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