Mathematical Proceedings of the Cambridge Philosophical Society

A Legendrian surgery presentation of contact 3-manifolds

a1 Department of Mathematics, Peking University, Beijing 100871, P. R. China. e-mail:
a2 Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany. e-mail:

Article author query
ding f   [Google Scholar] 
geiges h   [Google Scholar] 


We prove that every closed, connected contact 3-manifold can be obtained from $S^3$ with its standard contact structure by contact (${\pm}1$)-surgery along a Legendrian link. As a corollary, we derive a result of Etnyre and Honda about symplectic cobordisms (in a slightly stronger form).

(Received January 29 2003)