Noncommutative homological mirror functor

Cheol-Hyun Cho Seoul National University Hansol Hong The Chinese University of Hong Kong Siu-Cheong Lau Boston University

Symplectic Geometry mathscidoc:1605.15002

Memoirs of the American Mathematical Society
We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural functor from the Fukaya category to the category of matrix factorizations of the constructed Landau-Ginzburg model. As applications, it is applied to elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds to construct their mirrors and functors. In particular it recovers and strengthens several interesting results of Etingof-Ginzburg, Bocklandt and Smith, and gives a unified understanding of their results in terms of mirror symmetry and symplectic geometry. As an interesting application, we construct an explicit global deformation quantization of an affine del Pezzo surface as a noncommutative mirror to an elliptic orbifold.
mirror symmetry, noncommutative geometry, homological, functor, SYZ, quiver, Hitchin system, pillowcase
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  title={Noncommutative homological mirror functor},
  author={Cheol-Hyun Cho, Hansol Hong, and Siu-Cheong Lau},
  booktitle={Memoirs of the American Mathematical Society},
Cheol-Hyun Cho, Hansol Hong, and Siu-Cheong Lau. Noncommutative homological mirror functor. In Memoirs of the American Mathematical Society.
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