Quantum Structures for Lagrangian Submanifolds

Abstract

We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.

193 pages, 28 figures

References in corpus (3)

• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Quantum cohomology of complete intersections
• Products of Floer cohomology of torus fibers in toric Fano manifolds

Cited by in corpus (51)

• Rigid subsets of symplectic manifolds
• Rigidity and uniruling for Lagrangian submanifolds
• Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle
• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• On Exotic Lagrangian Tori in CP^2
• Bounds on spectral norms and barcodes
• Homological Lagrangian monodromy
• Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds
• A symplectic Gysin sequence
• The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory
• Floer homology of Lagrangians in clean intersection
• Lagrangian Floer theory on compact toric manifolds: survey
• Open strings, Lagrangian conductors and Floer functor
• Open Gromov-Witten invariants in dimension six
• Quantitative Heegaard Floer cohomology and the Calabi invariant
• Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds
• Low-area Floer theory and non-displaceability
• Fukaya algebras via stabilizing divisors
• Source Spaces and Perturbations for Cluster Complexes
• Higher rank local systems in Lagrangian Floer theory
• Categorification of Seidel's representation
• Invariants of Lagrangian cobordisms via spectral numbers
• Canonical models of filtered $A_{\infty }$-algebras and Morse complexes
• Localized mirror functor constructed from a Lagrangian torus
• Lagrangian Cobordism I
• Structure of $J$-holomorphic disks with immersed Lagrangian boundary conditions
• On the quantum homology algebra of toric Fano manifolds
• A monotone Lagrangian casebook
• $T$-equivariant disc potentials for toric Calabi-Yau manifolds
• Pairings in mirror symmetry between a symplectic manifold and a Landau-Ginzburg $B$-model
• An open quantum Kirwan map
• Lagrangian Quantum Homology for Lagrangian cobordism
• Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
• Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry
• Symplectic embeddings and continued fractions: a survey
• On the degenerated Arnold-Givental conjecture
• Superfiltered $A_{\infty }$-deformations of the exterior algebra, and local mirror symmetry
• Disjoinable Lagrangian tori and semisimple symplectic cohomology
• Floer cohomology and pencils of quadrics
• Fukaya categories of Lagrangian cobordisms and duality
• Holomorphic disks and the disk potential for a fibered Lagrangian
• Piunikhin-Salamon-Schwarz isomorphisms and spectral invariants for conormal bundle
• Generating the Fukaya categories of compact toric varieties
• Twin Lagrangian fibrations in mirror symmetry
• An explicit construction of a maximal relative symplectic packing of the Clifford torus
• Immersed Lagrangian Floer cohomology via pearly trajectories
• Lagrangian intersections and a conjecture of Arnol'd
• Action selectors and Maslov class rigidity
• The fundamental group of a rigid Lagrangian cobordism
• Morse Homology for the Yang-Mills Gradient Flow
• Dehn-Seidel twist, $C^0$ symplectic topology and barcodes