Géométrie de contact: de la dimension trois vers les dimensions supérieures

Abstract

On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry of closed contact manifolds and the geometry of compact symplectic Stein manifolds that they bound. The origin of these relations is the existence of open book decompositions adapted to contact structures.

Cited by in corpus (168)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• Lectures on open book decompositions and contact structures
• A Legendrian surgery presentation of contact 3-manifolds
• Brieskorn manifolds in contact topology
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Stabilization in the braid groups II: Transversal simplicity of knots
• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• Khovanov module and the detection of unlinks
• On the stable equivalence of open books in three-manifolds
• Constructing Lefschetz-type fibrations on four-manifolds
• Planar open books, monodromy factorizations, and symplectic fillings
• Real map germs and higher open books
• The vanishing of the contact invariant in the presence of torsion
• Sutures and contact homology I
• Overtwisted open books from sobering arcs
• Legendrian Fronts for Affine Varieties
• Altering symplectic manifolds by homologous recombination
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• A class of non-fillable contact structures
• Lecture notes on stabilization of contact open books
• Seifert fibered contact three-manifolds via surgery
• Homological mirror symmetry for log Calabi-Yau surfaces
• Instantons and L-space surgeries
• The algebraic crossing number and the braid index of knots and links
• On generalizing Lutz twists
• Open books and the Weinstein conjecture
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Kahler decomposition of 4-manifolds
• Maximal contact and symplectic structures
• Braided embeddings of contact 3-manifolds in the standard contact 5-sphere
• Contact Homology of Orbit Complements and Implied Existence
• A combinatorial description of the Heegaard Floer contact invariant
• Simplifying indefinite fibrations on 4-manifolds
• Contact structures on 5-manifolds
• Loose Legendrians and the plastikstufe
• Convex hypersurface theory in contact topology
• A biased view of symplectic cohomology
• Planar open books and Floer homology
• Contact handles, duality, and sutured Floer homology
• Open book decompositions for contact structures on Brieskorn manifolds
• Mapping class group relations, Stein fillings, and planar open book decompositions
• Almost contact 5-folds are contact
• Reeb foliations on S^5 and contact 5-manifolds violating the Thurston-Bennequin inequality
• Heegaard splittings and open books
• First steps in stable Hamiltonian topology
• On Legendrian Graphs
• Planar open books with four binding components
• Quasipositive links and Stein surfaces
• Constructions of Morse maps for knots and links, and upper bounds on the Morse-Novikov number
• Holomorphic curves in the presence of holomorphic hypersurface foliations
• Transverse Surgery on Knots in Contact 3-Manifolds
• Non-looseness of non-loose knots
• Positive factorizations of mapping classes
• Floer Cohomology, Multiplicity and the Log Canonical Threshold
• The Self-Linking Number in Annulus and Pants Open Book Decompositions
• Computability and the growth rate of symplectic homology
• Bypass attachments in higher-dimensional contact topology
• Holomorphic Open Book Decompositions
• Problems around 3-manifolds
• Diagrams for contact 5-manifolds
• Constructions of contact forms on products and piecewise fibered manifolds
• On the transverse invariant for bindings of open books
• On the support genus of a contact structure
• Lectures on Contact Geometry in Low-Dimensional Topology
• Symplectic hypersurfaces and transversality in Gromov-Witten theory
• On some examples and constructions of contact manifolds
• Contact Structures on Plumbed 3-Manifolds
• The Weinstein Conjecture for Planar Contact Structures in Dimension Three
• Lefschetz fibrations over the disc
• Symplectic Mapping Class Group Relations Generalizing the Chain Relation
• Contact surgery on the Hopf link: classification of fillings
• Planar Contact Structures with Binding Number Three
• Contact 3-manifolds, holomorphic curves and intersection theory
• Foliated Open Books
• Stein fillings of contact 3-manifolds obtained as Legendrian surgeries
• The contact invariant in sutured Floer homology
• Salem-Boyd sequences and Hopf plumbing
• Getting a handle on contact manifolds
• An introduction to Weinstein handlebodies for complements of smoothed toric divisors
• Embeddings of $3$--manifolds via open books
• On properties of Bourgeois contact structures
• Non-fillable invariant contact structures on principal circle bundles and left-handed twists
• Open books for Boothby-Wang bundles, fibered Dehn twists and the mean Euler characteristic
• On the relative Giroux correspondence
• Infinitely many universally tight torsion free contact structures with vanishing Ozsváth-Szabó contact invariants
• Braiding link cobordisms and non-ribbon surfaces
• On Transverse Knots and Branched Covers
• Capping off open books and the Ozsvath-Szabo contact invariant
• Montesinos knots, Hopf plumbings, and L-space surgeries
• Lefschetz Fibrations on Compact Stein Manifolds
• Generalizations of planar contact manifolds to higher dimensions
• Open book decompositions of fibre sums in contact topology
• A spectral sequence for symplectic homology
• Spaces of tight contact structures in dimension 3
• Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants
• Contactomorphism groups and Legendrian flexibility
• Existence of Engel structures
• Equivariant symplectic homology and multiple closed Reeb orbits
• Algebraic torsion via Heegaard Floer homology
• Braids, knots and contact structures
• Ricci Curvature, Reeb Flows and Contact 3-Manifolds
• Contact open books with flexible pages
• Stein fillable contact 3-manifolds and positive open books of genus one
• The topology and geometry of contact structures in dimension three
• The Reeb foliation arises as a family of Legendrian submanifolds at the end of a deformation of the standard S^3 in S^5
• Weinstein handlebodies for complements of smoothed toric divisors
• Invariants of Legendrian knots from open book decompositions
• Stein fillings of homology $3$-spheres and mapping class groups
• Contact structures on M \times S^2
• The support genus of certain Legendrian knots
• Flat plumbing basket and contact structure
• Global surfaces of section for Reeb flows in dimension three and beyond
• The arc complex and contact geometry: non-destabilizable planar open book decompositions of the tight contact 3-sphere
• Legendrian Realization in Convex Lefschetz Fibrations and Convex Stabilizations
• A note on Mitsumatsu's construction of a leafwise symplectic foliation
• Homotopy theoretic properties of open books
• On the Classification of Planar Contact Structures
• Local geometry of symplectic divisors with applications to contact torus bundles
• Flat plumbing basket, self-linking number and Thurston-Bennequin number
• Two applications of twisted Floer homology
• Classification of tight contact structures on small Seifert 3-manifolds with e_0\geq 0
• Codimension one foliations calibrated by non-degenerate closed 2-forms
• Realizing 4-manifolds as achiral Lefschetz fibrations
• Transverse knots, branched double covers and Heegaard Floer contact invariants
• Nested open books and the binding sum
• On the extrinsic geometry of contact structures
• On Legendrian Embbeddings into Open Book Decompositions
• 5-dimensional Bourgeois contact structures are tight
• Maximal Page Crossing Numbers of Legendrian Surfaces in Closed Contact 5-Manifolds
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology
• Algebraic links in lens spaces
• Whitehead's Integral Formula, Isolated Critical Points, and the Enhancement of the Milnor Number
• Symplectic fillings of virtually overtwisted contact structures on lens spaces
• Existence of coLegendrians in contact $5$-manifolds
• Contact structures on product five-manifolds and fibre sums along circles
• Combinatorial proofs for basic properties of Ozsvath-Szabo invariant
• Minimal contact triangulations of 3-manifolds
• S-stable foliations on flow-spines with transverse Reeb flow
• Dirac spectral flow on contact three manifolds II: Thurston--Winkelnkemper contact forms
• Umbilic Singularities and Lines of Curvature on Ellipsoids of ${\mathbb{R}}^4$
• Positive factorizations of pseudoperiodic homeomorphisms
• Taubes's proof of the Weinstein conjecture in dimension three
• Monoids in the mapping class group
• Torsion and Open Book Decompositions
• Ozsvath-Szabo invariants and fillability of contact structures
• Tunnel One, Fibered Links
• Complete classification of generalized crossing changes between GOF-knots
• Contact structures on 3-manifolds are deformations of foliations
• Open books supporting overtwisted contact structures and Stallings twist
• Elliptic open books on torus bundles over the circle
• Finite Energy Foliations on Overtwisted Contact Manifolds
• Surgery diagrams for horizontal contact structures
• Invariants of contact structures from open books
• Some 3-dimensional transverse C-links (Constructions of higher-dimensional C-links, I)
• Factorizations in SL(2,Z) and simple examples of inequivalent Stein fillings
• Giroux correspondence, confoliations, and symplectic structures on S^1 x M
• Constructing broken Lefschetz fibrations from handle decompositions
• A note on stabilization heights of fiber surfaces and the Hopf invariants
• Examples of non-minimal open books with high fractional Dehn twist coefficient
• On the relative slice Thurston-Bennequin inequality
• Homological invariants of codimension 2 contact submanifolds
• On overtwisted, right-veering open books
• Periodic Surface Homeomorphisms and Contact Structures
• On naturality of the Ozsvath-Szabo contact invariant
• On open books and embedding of smooth and contact manifolds
• Transverse links, open books and overtwisted manifolds
• Open books and exact symplectic cobordisms