Rigidity and uniruling for Lagrangian submanifolds

Abstract

This paper explores the topology of monotone Lagrangian submanifolds $L$ inside a symplectic manifold $M$ by exploiting the relationships between the quantum homology of $M$ and various quantum structures associated to the Lagrangian $L$.

In part, a shortened and revised version of "Quantum Structures for Lagrangian Submanifolds" (arXiv:0708.4221). Contains also new results

References in corpus (6)

• Rigid subsets of symplectic manifolds
• Quantum Structures for Lagrangian Submanifolds
• Mini-max theory, spectral invariants and geometry of the Hamiltonian diffeomorphism group
• Hamiltonian S^1 manifolds are uniruled
• An explicit construction of a maximal relative symplectic packing of the Clifford torus
• Cluster Homology

Cited by in corpus (58)

• Rigid subsets of symplectic manifolds
• Persistent homology and Floer-Novikov theory
• The monotone wrapped Fukaya category and the open-closed string map
• Bounds on spectral norms and barcodes
• Lagrangian Topology and Enumerative Geometry
• Quasi-morphisms on contactomorphism groups and contact rigidity
• On Certain Lagrangian Submanifolds of $S^2\times S^2$ and $C{P}^n$
• Symplectic quasi-states on the quadric surface and Lagrangian submanifolds
• Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds
• The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory
• Rabinowitz Floer homology and mirror symmetry
• Floer theory and flips
• Floer homology of Lagrangians in clean intersection
• Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
• Punctured holomorphic curves and Lagrangian embeddings
• Quasi-morphisms and quasi-states in symplectic topology
• Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory
• Disjoinable Lagrangian spheres and dilations
• Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties
• On an exotic Lagrangian torus in $\mathbb{C}{P}^2$
• Lagrangian blow-ups, blow-downs, and applications to real packing
• 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
• Generating the Fukaya categories of Hamiltonian G-manifolds
• Displacing Lagrangian toric fibers by extended probes
• Bounding Lagrangian widths via geodesic paths
• Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces
• Lagrangian Circle Actions
• Categorification of Seidel's representation
• The closed-open string map for $S^1$-invariant Lagrangians
• Invariants of Lagrangian cobordisms via spectral numbers
• Coisotropic Ekeland-Hofer capacities
• Lagrangian cobordism in Lefschetz fibrations
• Lagrangian Cobordism I
• Remarks on Lagrangian intersections in toric manifolds
• A Chiang-type Lagrangian in CP2
• Products and connected sums of spheres as monotone Lagrangian submanifolds
• Lagrangian Floer homology of the Clifford torus and real projective space in odd dimensions
• Riemannian distance and symplectic embeddings in cotangent bundle
• Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds
• A monotone Lagrangian casebook
• Hamiltonian unknottedness of certain monotone Lagrangian tori in $S^2\times S^2$
• Floer cohomology and pencils of quadrics
• Disjoinable Lagrangian tori and semisimple symplectic cohomology
• Displacement energy of compact Lagrangian submanifold from open subset
• Gromov width and uniruling for orientable Lagrangian surfaces
• Function theoretical applications of Lagrangian spectral invariants
• On the Existence of Symplectic Barriers
• Notes on monotone Lagrangian twist tori
• Zoo of monotone Lagrangians in $\mathbb{C}{P}^n$
• On the cohomology ring of narrow Lagrangian 3-manifolds, quantum Reidemeister torsion, and the Landau-Ginzburg superpotential
• A symplectic prolegomenon
• Monotone Lagrangian Floer theory in smooth divisor complements: I
• A Note On Lagrangian Vanishing Sphere Bundles
• Lagrangian intersections and a conjecture of Arnol'd
• On the Hofer-Zehnder conjecture for semipositive symplectic manifolds
• Poisson brackets and symplectic invariants
• The fundamental group of a rigid Lagrangian cobordism