Counting pseudo-holomorphic discs in Calabi-Yau 3 fold

Abstract

n this paper we define an invariant of a pair of 6 dimensional symplectic %optional manifold with vanishing 1st Chern class and its Lagrangian submanifold with vanishing Maslov index. This invariant is a function on the set of the path connected components of the bounding cochains (solution of A infinity version of Maurer-Cartan equation of the filtered A infinity algebra associated to the Lagrangian submanifold). In the case when the Lagrangian submanifold is a rational homology sphere, it becomes a numerical invariant. This invariant depends on the choice of almost complex structure. The way how it depends on the almost complex structure is described by a wall crossing formula which involves moduli space of pseudo-holomorphic spheres.

References in corpus (5)

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• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
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Cited by in corpus (10)

• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Counting genus zero real curves in symplectic manifolds
• Lagrangian Floer theory on compact toric manifolds: survey
• Conjectures on counting associative 3-folds in $G_2$-manifolds
• Notes on Kontsevich-Soibelman's theorem about cyclic A-infinity algebras
• Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
• Open Mirror Symmetry for Higher Dimensional Calabi-Yau Hypersurfaces
• Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds with Three Deformations
• Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds