Gluing Localized Mirror Functors

Abstract

We develop a method of gluing the local mirrors and functors constructed from immersed Lagrangians in the same deformation class. As a result, we obtain a global mirror geometry and a canonical mirror functor. We apply the method to construct the mirrors of punctured Riemann surfaces and show that our functor derives homological mirror symmetry.

arXiv comment69 pages, 39 figures, comments are welcome

References in corpus (1)

• Matrix factorizations for nonaffine LG-models

Cited by in corpus (7)

• Immersed two-spheres and SYZ with Application to Grassmannians
• On the Complex Affine Structures of SYZ Fibration of Del Pezzo Surfaces
• $T$-equivariant disc potentials for toric Calabi-Yau manifolds
• Fukaya categories of higher-genus surfaces and pants decompositions
• Big Quantum cohomology of orbifold spheres
• Cyclic group actions on Fukaya categories and mirror symmetry
• Maurer-Cartan deformation of Lagrangians