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Noncommutative Homological Mirror Functor
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eBook
Noncommutative Homological Mirror Functor
2021
Overview
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.
Publisher
American Mathematical Society
Subject
ISBN
9781470447618, 1470447614
