Coisotropic intersections

DOI10.1215/S0012-7094-07-14014-6zbMath1129.53062arXivmath/0605186OpenAlexW3036998574WikidataQ56813193 ScholiaQ56813193MaRDI QIDQ2458991

Viktor L. Ginzburg

Publication date: 5 November 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605186

zbMATH Keywords

Hamiltonian diffeomorphismLagrangian submanifoldsymplectic manifolddisplacementcharacteristic foliationHofer metriccoisotropic submanifoldsymplectic areafiltered Floer homologyaction selectorcoisotropic Liouville classLagrangian (resp. coisotropic) intersection propertyleafwise intersection propertysubcritical Stein manifold

Mathematics Subject Classification ID

Related Items (25)

ON MAGNETIC LEAF-WISE INTERSECTIONS ⋮ Action and index spectra and periodic orbits in Hamiltonian dynamics ⋮ Hamiltonian pseudo-rotations of projective spaces ⋮ Rabinowitz Floer Homology: A Survey ⋮ On the rigidity of the coisotropic Maslov index on certain rational symplectic manifolds ⋮ Künneth formula in Rabinowitz Floer homology ⋮ Translated points on hypertight contact manifolds ⋮ Closed Reeb orbits on the sphere and symplectically degenerate maxima ⋮ The Conley conjecture ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ ON ITERATED TRANSLATED POINTS FOR CONTACTOMORPHISMS OF ℝ²ⁿ⁺¹ AND ℝ²ⁿ × S¹ ⋮ Coisotropic Ekeland–Hofer capacities ⋮ Hyperbolic fixed points and periodic orbits of Hamiltonian diffeomorphisms ⋮ Submanifolds and the Hofer norm ⋮ LEAF-WISE INTERSECTIONS AND RABINOWITZ FLOER HOMOLOGY ⋮ Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds ⋮ Existence of leafwise intersection points in the unrestricted case ⋮ Bounding Lagrangian widths via geodesic paths ⋮ Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds ⋮ TOTALLY NON-COISOTROPIC DISPLACEMENT AND ITS APPLICATIONS TO HAMILTONIAN DYNAMICS ⋮ Cup-length estimates for leaf-wise intersections ⋮ Fragility and persistence of leafwise intersections ⋮ Three examples in the dynamical systems theory ⋮ Coisotropic rigidity and \(C^0\)-symplectic geometry ⋮ Iterated index and the mean Euler characteristic

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lagrangian submanifolds and Hamiltonian systems
• Symplectic topology as the geometry of generating functions
• Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic sub\-manifolds
• Geometry of contact transformations and domains: orderability versus squeezing
• Two symplectic fixed-point theorems with applications to Hamiltonian dynamics
• Hamiltonian dynamics on convex symplectic manifolds
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Pseudo holomorphic curves in symplectic manifolds
• Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent
• A proof of Weinstein's conjecture in \(\mathbb R^{2n}\)
• Periodic solutions on hypersurfaces and a result by C. Viterbo
• Morse theory for Lagrangian intersections
• Witten's complex and infinite dimensional Morse theory
• On fixed points of symplectic maps
• A fixed point theorem in symplectic geometry
• Floer homology and Arnold conjecture
• Arnold conjecture and Gromov-Witten invariant
• Symplectic homology. I: Open sets in \(\mathbb{C}^ n\)
• Holomorphic curves in symplectic geometry
• Applications of symplectic homology. I
• Symplectic boundaries: Creating and destroying closed characteristics
• Gromov-Floer theory and disjunction energy of compact Lagrangian embeddings
• A contact condition for \(p\)-codimensional submanifolds of a symplectic manifold \((2\leq p\leq n)\)
• Exact Lagrange submanifolds, periodic orbits and the cohomology of free loop spaces
• Propagation in Hamiltonian dynamics and relative symplectic homology
• Length minimizing Hamiltonian paths for symplectically aspherical manifolds.
• A \(C^2\)-smooth counterexample to the Hamiltonian Seifert conjecture in \(\mathbb R^4\)
• On the action spectrum for closed symplectically aspherical manifolds
• Hofer-Zehnder capacity and length minimizing Hamiltonian paths
• Lagrangian embeddings into subcritical Stein manifolds
• Chain level Floer theory and Hofer's geometry of the Hamiltonian diffeomorphism group.
• Symplectic fixed points and holomorphic spheres
• The geometry of symplectic energy
• New smooth counterexamples to the Hamiltonian Seifert conjecture.
• Symplectic homology and periodic orbits near symplectic submanifolds
• Relative Hofer-Zehnder capacity and periodic orbits in twisted cotangent bundles
• Transversality in elliptic Morse theory for the symplectic action
• Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. II
• Functors and computations in Floer homology with applications. I
• Lagrangian intersections, symplectic energy, and areas of holomorphic curves
• Applications of Hofer's geometry to Hamiltonian dynamics
• Symplectic manifolds and their Lagrangian submanifolds
• Symplectic displacement energy for Lagrangian submanifolds
• On the topological properties of symplectic maps
• TOTALLY NON-COISOTROPIC DISPLACEMENT AND ITS APPLICATIONS TO HAMILTONIAN DYNAMICS
• The unregularized gradient flow of the symplectic action
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• The weinstein conjecture in the presence of holomorphic spheres
• THE WEINSTEIN CONJECTURE ON SOME SYMPLECTIC MANIFOLDS CONTAINING THE HOLOMORPHIC SPHERES
• Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I
• Cuplength estimates on lagrangian intersections
• Symplectic rigidity, symplectic fixed points, and global perturbations of Hamiltonian systems
• Finiteness of the Hofer-Zehnder capacity of neighborhoods of symplectic submanifolds
• Existence of periodic solutions of Hamiltonian systems on almost every energy surface
• K-area, Hofer metric and geometry of conjugacy classes in Lie groups.

This page was built for publication: Coisotropic intersections