### Abstract

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 and prove homological mirror symmetry. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space.

Original language | English |
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Pages (from-to) | 284-320 |

Number of pages | 37 |

Journal | Journal of Geometry and Physics |

Volume | 136 |

DOIs | |

Publication status | Published - 2019 Feb |

### All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

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## Cite this

Cho, C. H., Hong, H., & Lau, S. C. (2019). Localized mirror functor constructed from a Lagrangian torus.

*Journal of Geometry and Physics*,*136*, 284-320. https://doi.org/10.1016/j.geomphys.2018.11.006