### 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 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Geometry and Physics*,

*136*, 284-320. https://doi.org/10.1016/j.geomphys.2018.11.006

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

**Localized mirror functor constructed from a Lagrangian torus.** / Cho, Cheol Hyun; Hong, Hansol; Lau, Siu Cheong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Localized mirror functor constructed from a Lagrangian torus

AU - Cho, Cheol Hyun

AU - Hong, Hansol

AU - Lau, Siu Cheong

PY - 2019/2

Y1 - 2019/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85058631221&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058631221&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2018.11.006

DO - 10.1016/j.geomphys.2018.11.006

M3 - Article

AN - SCOPUS:85058631221

VL - 136

SP - 284

EP - 320

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -