Symplectic topology in the nineties

DOI10.1016/S0926-2245(98)00018-7zbMath0955.57024OpenAlexW2036516962WikidataQ115337487 ScholiaQ115337487MaRDI QIDQ1295462

Ya. M. Ehliashberg

Publication date: 28 September 2000

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0926-2245(98)00018-7

zbMATH Keywords

Seiberg-Witten invariantsHamiltonian dynamicscontact manifoldssymplectic rigiditygenerating families

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Symplectic and contact topology in high or arbitrary dimension (57R17) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02)

Related Items

Cylindrical contact homology of subcritical Stein-fillable contact manifolds, Entropies from coarse-graining: convex polytopes vs. ellipsoids, No homotopy 4-sphere invariants using ECH=SWF, On the uniqueness of Hofer's geometry, Stein fillability and the realization of contact manifolds, Plane fields related to vector fields on 3-manifolds, Contact cuts, Unnamed Item

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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fourier integral operators. I
• Symplectic diffeomorphisms as isometries of Hofer's norm
• Some integration problems in almost-complex and complex manifolds
• Symplectic manifolds with contact type boundaries
• WEINSTEIN CONJECTURE AND GW-INVARIANTS
• SEIBERG–WITTEN INVARIANTS FOR MANIFOLDS WITH b₊=1 AND THE UNIVERSAL WALL CROSSING FORMULA
• Symplectic displacement energy for Lagrangian submanifolds
• On the topological properties of symplectic maps
• The Structure of Rational and Ruled Symplectic 4-Manifolds
• Envelopes of Holomorphy of Certain 2-Spheres in C 2*
• New Invariants of Open Symplectic and Contact Manifolds
• TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2
• A symplectic fixed point theorem for complex projective spaces
• The unregularized gradient flow of the symplectic action
• A relative morse index for the symplectic action
• First steps in symplectic topology
• Partial Differential Relations
• On the Envelope of Holomorphy of a 2-Sphere in ℂ 2
• The weinstein conjecture in the presence of holomorphic spheres
• Shorter Notes: Some Simple Examples of Symplectic Manifolds
• Periodic solutions of hamiltonian systems
• Quantum cohomology of projective bundles over ℙⁿ
• From symplectic deformation to isotopy
• BIINVARIANT METRICS ON THE GROUP OF HAMILTONIAN DIFFEOMORPHISMS
• Gromov's Compactness Theorem for Pseudo Holomorphic Curves
• Une structure de contact, même tendue, est plus ou moins tordue
• Lectures on Gromov invariants for symplectic 4-manifolds
• A smooth counterexample to the Hamiltonian Seifert conjecture in R^6
• Tight contact structures on solid tori
• Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
• Corrigenda to: Introduction to Symplectic Topology
• Homological Algebra of Mirror Symmetry
• Equivariant Gromov - Witten Invariants
• On the Volume Elements on a Manifold
• SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves
• Connectedness of spaces of symplectic embeddings
• Diffeomorphisms of the 2-Sphere
• Foliations and the topology of 3-manifolds
• A mathematical theory of quantum cohomology
• Examples of symplectic structures
• The classification of ruled symplectic 4-manifolds
• Critical points of quasi-functions and generating families of Legendrian manifolds
• Irreducible 4-manifolds need not be complex
• Lagrangian submanifolds and Hamiltonian systems
• Some global properties of contact structures
• Symplectic topology and Hamiltonian dynamics. II
• Blow ups and symplectic embeddings in dimension 4
• Hamiltonian systems, Lagrangian tori and Birkhoff's theorem
• Symplectic topology as the geometry of generating functions
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Lagrangian embeddings and critical point theory
• Pseudo holomorphic curves in symplectic manifolds
• Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent
• Periodic solutions on hypersurfaces and a result by C. Viterbo
• A theorem on the structure of wave fronts and its applications in symplectic topology
• The Weinstein conjecture in \(P\times {\mathbb{C}}^{\ell}\)
• Lusternik-Schnirelman-theory for Lagrangian intersections
• Morse theory for Lagrangian intersections
• Witten's complex and infinite dimensional Morse theory
• Mirror principle. I
• Periodic solutions of Hamiltonian system on a prescribed energy surface
• Lagrange and Legendre cobordisms. II
• Supersymmetry and Morse theory
• Lagrangian submanifolds and exact Lagrangians of cotangent bundles
• Contact surgery and symplectic handlebodies
• Singularities of \(J\)-holomorphic curves in almost complex 4-manifolds
• Convexité en topologie de contact. (Convexity in contact topology)
• Towards the definition of symplectic boundary
• Contact 3-manifolds twenty years since J. Martinet's work
• Pseudo-holomorphic maps and bubble trees
• Structures de contact sur les fibrés principaux en cercles de dimension trois
• Sur la géométrie des structures de contact invariantes
• On the hypotheses of Rabinowitz' periodic orbit theorems
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Symplectic fillings and positive scalar curvature
• Floer homology and Arnold conjecture
• Symplectic four-manifolds and projective surfaces
• A complete proof of Viterbo's uniqueness theorem on generating functions
• Symplectic topology and extremal rays
• Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three
• Coherent orientations for periodic orbit problems in symplectic geometry
• The Maslov index for paths
• Symplectic homology. I: Open sets in \(\mathbb{C}^ n\)
• Symplectic topology on algebraic 3-folds
• Holomorphic curves in symplectic geometry
• A Hamiltonian characterization of the three-ball
• Symplectic geometry: an introduction based on the seminar in Bern, 1992
• Symplectic normal connect sum
• Isotopy of symplectic balls, Gromov's radius and the structure of ruled symplectic 4-manifolds
• A geometric heat flow for one-forms on three dimensional manifolds
• Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms
• Applications of symplectic homology. I
• Symplectic homology. II: A general construction
• Gromov's compactness theorem for pseudo-holomorphic curves
• Symplectic boundaries: Creating and destroying closed characteristics
• Lagrangian tori in a symplectic vector space and global symplectomorphisms
• Symplectic submanifolds and almost-complex geometry
• Counting pseudo-holomorphic submanifolds in dimension 4
• Applications of contact surgery
• Symplectic packing in dimension 4
• Filling by holomorphic disks with weakly pseudoconvex boundary conditions
• Correction to ``A characterisation of the tight three-sphere
• Monopoles and contact structures
• Normal contact structures on 3-manifolds
• Higher genus symplectic invariants and sigma models coupled with gravity
• Estimates for the energy of a symplectic map
• Symplectic fixed points and holomorphic spheres
• Properties of pseudoholomorphic curves in symplectisations. I: Asymptotics
• Birational equivalence in the symplectic category
• Classification of overtwisted contact structures on 3-manifolds
• Problèmes d'intersections et de points fixes en géométrie hamiltonienne. (Intersection and fixed-point problems in Hamiltonian geometry)
• New applications of Luttinger's surgery
• The structure of branch points in minimal surfaces and in pseudoholomorphic curves
• The geometry of symplectic energy
• Symplectic gluing along hypersurfaces and resolution of isolated orbifold singularities
• Quantum cohomology of flag manifolds and Toda lattices
• On the Arnold conjecture for weakly monotone symplectic manifolds
• The genus of embedded surfaces in the projective plane
• The Seiberg-Witten invariants and symplectic forms
• Lagrangian intersections in contact geometry
• Properties of pseudo-holomorphic curves in symplectisations. II: Embedding controls and algebraic invariants
• Local non-squeezing theorems and stability
• More constraints on symplectic forms from Seiberg-Witten invariants
• Four-manifolds without symplectic structures but with nontrivial Seiberg-Witten invariants
• Bott-type symplectic Floer cohomology and its multiplication structures
• Symplectic structure on ruled surfaces and a generalized adjunction formula
• A new construction of symplectic manifolds
• Transversality in elliptic Morse theory for the symplectic action
• Symplectic engulfing and Lagrangian intersections
• Hopf-type rigidity for Newton equations
• General wall crossing formula
• A characterisation of the tight three-sphere
• Lagrangian tori in \(\mathbb{R}^ 4\)
• Topological sigma model and Donaldson-type invariants in Gromov theory
• Gromov's K-area and symplectic rigidity
• Local Lagrangian 2-knots are trivial
• Conjugate points on geodesics of Hofer's metric
• Lagrangian intersections, symplectic energy, and areas of holomorphic curves
• Applications of symplectic homology. II: Stability of the action spectrum