Localized mirror functor constructed from a Lagrangian torus

Cheol Hyun Cho, Hansol Hong, Siu Cheong Lau

Research output: Contribution to journalArticle


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 languageEnglish
Pages (from-to)284-320
Number of pages37
JournalJournal of Geometry and Physics
Publication statusPublished - 2019 Feb

All Science Journal Classification (ASJC) codes

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

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