Topological Fukaya category and mirror symmetry for punctured surfaces

Abstract

In this paper we establish a version of homological mirror symmetry for punctured Riemann surfaces. Following a proposal of Kontsevich we model A-branes on a punctured surface $\Sigma$ via the topological Fukaya category. We prove that the topological Fukaya category of $\Sigma$ is equivalent to the category of matrix factorizations of the mirror LG model $(X,W)$. Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which might be of independent interest.

45 pages, 7 figures. v4: revised remarks on partially wrapped cases

References in corpus (23)

• Higher Topos Theory
• Triangulated categories of singularities and D-branes in Landau-Ginzburg models
• Flat surfaces and stability structures
• Matrix factorizations for nonaffine LG-models
• Triangulated surfaces in triangulated categories
• Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over $\bar{Q}$
• Homological Mirror Symmetry for manifolds of general type
• Wrapped microlocal sheaves on pairs of pants
• Thom-Sebastiani & Duality for Matrix Factorizations
• Moduli of Tropical Plane Curves
• Arboreal Singularities
• The nonequivariant coherent-constructible correspondence for toric stacks
• Rectification of enriched infinity-categories
• Differential Graded Categories are k-linear Stable Infinity Categories
• Auslander orders over nodal stacky curves and partially wrapped Fukaya categories
• Skeleta of Affine Hypersurfaces
• Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions
• Compact generation of the category of D-modules on the stack of G-bundles on a curve
• Topological recursion and mirror curves
• A1-homotopy invariants of topological Fukaya categories of surfaces
• Cyclic symmetries of A_n-quiver representations
• A combinatorial calculation of the Landau-Ginzburg model $M={\mathbb{C}}^3,W=z_1{z}_2{z}_3$
• Microlocal Category

Cited by in corpus (15)

• Flat surfaces and stability structures
• The nonequivariant coherent-constructible correspondence for toric stacks
• Mirror symmetry for very affine hypersurfaces
• Auslander orders over nodal stacky curves and partially wrapped Fukaya categories
• Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions
• Lagrangian Skeleta of Hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
• Perverse sheaves of categories and some applications
• Mirror symmetry for honeycombs
• Moduli of Lagrangian immersions with formal deformations
• Lagrangian Cobordisms in Liouville manifolds
• A bordered HF- algebra for the torus
• Versality in mirror symmetry
• Fukaya categories of higher-genus surfaces and pants decompositions
• Line fields on punctured surfaces and twisted derived categories
• Strebel Differentials and stable Matrix Factorizations