A Legendrian surgery presentation of contact 3-manifolds

Abstract

We prove that every closed, connected contact 3-manifold can be obtained from the 3-sphere with its standard contact structure by contact surgery of coefficient plus or minus 1 along a Legendrian link. As a corollary, we derive a result of Etnyre and Honda about symplectic cobordisms (in slightly stronger form).

18 pages, Section 3 and three figures added. To appear in Math. Proc. Cambridge Philos. Soc

References in corpus (2)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Symplectic fillability of tight contact structures on torus bundles

Cited by in corpus (57)

• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• On the existence of tight contact structures on Seifert fibered 3-manifolds
• The vanishing of the contact invariant in the presence of torsion
• Constructing symplectic forms on 4-manifolds which vanish on circles
• Surgery diagrams for contact 3-manifolds
• Handle moves in contact surgery diagrams
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• Seifert fibered contact three-manifolds via surgery
• Every 4-Manifold is BLF
• How to recognise a 4-ball when you see one
• Tight contact structures on Seifert manifolds over T^2 with one singular fibre
• Maximal contact and symplectic structures
• Dehn surgery, rational open books and knot Floer homology
• The diffeotopy group of S^1 \times S^2 via contact topology
• Canonical contact structures on some singularity links
• Dehn Twists in Heegaard Floer Homology
• Contact surgery and supporting open books
• The Legendrian knot complement problem
• Infinitely many universally tight contact manifolds with trivial Ozsvath-Szabo contact invariants
• Computing rotation and self-linking numbers in contact surgery diagrams
• On the support genus of a contact structure
• Contact Structures on Plumbed 3-Manifolds
• Ozsváth-Szabó invariants of contact surgeries
• Legendrian Hopf links
• Planar Contact Structures with Binding Number Three
• Knot Floer homology detects genus-one fibred knots
• Classification of tight contact structures on surgeries on the figure-eight knot
• Contact surgery and symplectic caps
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• On Transverse Knots and Branched Covers
• Capping off open books and the Ozsvath-Szabo contact invariant
• Stein traces and characterizing slopes
• An open book decomposition compatible with rational contact surgery
• Round surgery and contact structures on 3-manifolds
• Invariants of Legendrian knots from open book decompositions
• Contact (+1)-surgeries along Legendrian Two-component Links
• On contact surgery and knot Floer invariants
• Contact surgery graphs
• Legendrian knots and links classified by classical invariants
• Transverse knots, branched double covers and Heegaard Floer contact invariants
• Classification of tight contact structures on small Seifert 3-manifolds with e_0\geq 0
• Cosmetic contact surgeries along transverse knots and the knot complement problem
• On Contact Round Surgeries on $({\mathbb{S}}^3,{\xi }_{st})$ and Their Diagrams
• Contact Dehn surgery, symplectic fillings, and Property P for knots
• Contact surgery numbers of projective spaces
• Minimal contact triangulations of 3-manifolds
• Contact (+1)-surgeries on rational homology 3-spheres
• On the self-linking number of transverse links
• Explicit horizontal open books on some Seifert fibered 3--manifolds
• Admissible transverse surgery does not preserve tightness
• Lutz twist and contact surgery
• Smoothly non-isotopic Lagrangian disk fillings of Legendrian knots
• Tight contact structures on some small Seifert fibered 3--manifolds
• Notes on the contact Ozsvath--Szabo invariants
• Full Lutz twist along the binding of an open book
• On overtwisted, right-veering open books
• Legendrian Hopf links in L(p,1)