Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions

Abstract

Given a punctured Riemann surface with a pair-of-pants decomposition, we compute its wrapped Fukaya category in a suitable model by reconstructing it from those of various pairs of pants. The pieces are glued together in the sense that the restrictions of the wrapped Floer complexes from two adjacent pairs of pants to their adjoining cylindrical piece agree. The $A_{\infty }$-structures are given by those in the pairs of pants. The category of singularities of the mirror Landau-Ginzburg model can also be constructed in the same way from local affine pieces that are mirrors of the pairs of pants.

arXiv comment43 pages, 14 figures, comments welcome

References in corpus (8)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Homogeneous coordinate rings and mirror symmetry for toric varieties
• Matrix factorizations for nonaffine LG-models
• Homological Mirror Symmetry for manifolds of general type
• Fukaya categories of symmetric products and bordered Heegaard-Floer homology
• Family Floer cohomology and mirror symmetry
• Topological Fukaya category and mirror symmetry for punctured surfaces
• Fukaya Categories as Categorical Morse Homology

Cited by in corpus (11)

• Auslander orders over nodal stacky curves and partially wrapped Fukaya categories
• Topological Fukaya category and mirror symmetry for punctured surfaces
• Homological mirror symmetry at large volume
• Legendrian skein algebras and Hall algebras
• Partially wrapped Fukaya categories of simplicial skeleta
• Moduli of Lagrangian immersions with formal deformations
• Speculations on homological mirror symmetry for hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
• Fukaya categories of higher-genus surfaces and pants decompositions
• Homological mirror symmetry for elliptic Hopf surfaces
• Line fields on punctured surfaces and twisted derived categories
• Algebraic sheaves of Floer homology groups via algebraic torus actions on the Fukaya category