Geometry and Topology 12 (2008) 531–616

DOI: 10.2140/gt.2008.12.531

Abstract

We develop a method for preserving pseudoholomorphic curves in contact 3–manifolds under surgery along transverse links. This makes use of a geometrically natural boundary value problem for holomorphic curves in a 3–manifold with stable Hamiltonian structure, where the boundary conditions are defined by 1–parameter families of totally real surfaces. The technique is applied here to construct a finite energy foliation for every closed overtwisted contact 3–manifold.

Keywords

holomorphic curves, contact geometry, finite energy foliation, transverse surgery

Mathematical Subject Classification

Primary: 32Q65

Secondary: 57R17

References

Publication

Received: 19 November 2006
Accepted: 20 December 2007
Published: 12 March 2008
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Simon Donaldson

Authors