Floer homology of Lagrangian submanifolds

Abstract

This is a translation of an article appeared in Japanese in Suugaku 63 (2011), no. 1, 43-66 (MR2790665) and is a survey of Lagrangian Floer homology which the author studies jointly with Y.-G.Oh, H. Ohta, and K. Ono. It also contains some explanation on its relation to (homological) mirror symmetry.

arXiv comment29 pages

References in corpus (10)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Summing up D-Instantons
• Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Homogeneous coordinate rings and mirror symmetry for toric varieties
• Fukaya categories and deformations
• Homological mirror symmetry for the quartic surface
• Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle
• Kuranishi homology and Kuranishi cohomology
• From real affine geometry to complex geometry

Cited by in corpus (5)

• Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1
• Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m
• Conjectures on counting associative 3-folds in $G_2$-manifolds
• Manifolds with analytic corners
• Pati-Salam model in curved space-time from square root Lorentz manifold