Bounding Lagrangian widths via geodesic paths

DOI10.1112/S0010437X14007465zbMath1322.53082arXiv1307.1425WikidataQ125631466 ScholiaQ125631466MaRDI QIDQ5173076

Mark McLean, Matthew Strom Borman

Publication date: 6 February 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.1425

zbMATH Keywords

symplectic capacityLagrangian submanifoldsymplectic manifoldFloer cohomologysymplectic cohomologyLagrangian width

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12) Symplectic aspects of Floer homology and cohomology (53D40) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items

Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities ⋮ Relative Hofer-Zehnder capacity and positive symplectic homology ⋮ Exact Lagrangian caps and non-uniruled Lagrangian submanifolds ⋮ On Lagrangian embeddings of closed nonorientable 3-manifolds ⋮ Coisotropic rigidity and \(C^0\)-symplectic geometry ⋮ Gromov width and uniruling for orientable Lagrangian surfaces

Cites Work

• Unnamed Item
• Lagrangian caps
• Floer homology on the universal cover, Audin's conjecture and other constraints on Lagrangian submanifolds
• The embedding capacity of 4-dimensional symplectic ellipsoids
• On the wrapped Fukaya category and based loops
• Target-local Gromov compactness
• The Conley conjecture
• On Maslov class rigidity for coisotropic submanifolds
• Symplectic embeddings of ellipsoids in dimension greater than four
• A geometric refinement of a theorem of Chekanov
• A new obstruction to embedding Lagrangian tori
• An open string analogue of Viterbo functoriality
• Floer homology and the heat flow
• Rigidité symplectique dans le cotangent de \(T^ n\). (Symplectic rigidity on the cotangent bundle of \(T^ n)\)
• Spectral invariants in Lagrangian Floer theory
• Floer homology of cotangent bundles and the loop product
• Rigidity and uniruling for Lagrangian submanifolds
• Pseudo holomorphic curves in symplectic manifolds
• Morse theory for Lagrangian intersections
• Witten's complex and infinite dimensional Morse theory
• On the classification of Lagrange immersions
• On the Morse index in variational calculus
• A stability property of symplectic packing
• The Maslov index for paths
• Symplectic packings and algebraic geometry
• Symplectic homology. I: Open sets in \(\mathbb{C}^ n\)
• Applications of symplectic homology. I
• Propagation in Hamiltonian dynamics and relative symplectic homology
• Holomorphic curves and Hamiltonian systems in an open set with restricted contact-type boundary
• Symplectic fixed points and holomorphic spheres
• Transversality in elliptic Morse theory for the symplectic action
• A maximal relative symplectic packing construction
• Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry
• Functors and computations in Floer homology with applications. I
• Applications of symplectic homology. II: Stability of the action spectrum
• Packing symplectic manifolds by hand
• New obstructions to symplectic embeddings
• Coisotropic intersections
• Lagrangian intersections and the Serre spectral sequence
• Continuing 1-dimensional analytic sets
• Symplectic manifolds and their Lagrangian submanifolds
• Constructing exact Lagrangian immersions with few double points
• Some non-collarable slices of Lagrangian surfaces
• On the topological properties of symplectic maps
• Symplectic geometry and positivity of pseudo-differential operators
• On the Floer homology of cotangent bundles
• Cluster homology: An overview of the construction and results
• The unregularized gradient flow of the symplectic action
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I
• The Spectral Flow and the Maslov Index
• Addendum to “Floer Cohomology of Lagrangian Intersections and Pseudo‐Holomorphic Discs, I”
• Inner and outer hamiltonian capacities
• Symplectic rigidity, symplectic fixed points, and global perturbations of Hamiltonian systems
• Symplectic packing constructions