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