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 (23)

• Lectures on open book decompositions and contact structures
• The vanishing of the contact invariant in the presence of torsion
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• The algebraic crossing number and the braid index of knots and links
• Planar open books and Floer homology
• Constructions of Morse maps for knots and links, and upper bounds on the Morse-Novikov number
• Problems around 3-manifolds
• Lectures on Contact Geometry in Low-Dimensional Topology
• Symplectic hypersurfaces and transversality in Gromov-Witten theory
• The contact invariant in sutured Floer homology
• Salem-Boyd sequences and Hopf plumbing
• On Transverse Knots and Branched Covers
• Braids, knots and contact structures
• Classification of tight contact structures on small Seifert 3-manifolds with e_0\geq 0
• Open books supporting overtwisted contact structures and Stallings twist
• Ozsvath-Szabo invariants and fillability of contact structures
• Torsion and Open Book Decompositions
• Taubes's proof of the Weinstein conjecture in dimension three
• Combinatorial proofs for basic properties of Ozsvath-Szabo invariant
• On the extrinsic geometry of contact structures
• Giroux correspondence, confoliations, and symplectic structures on S^1 x M
• Finite Energy Foliations on Overtwisted Contact Manifolds
• Elliptic open books on torus bundles over the circle