Volume 12, issue 1 (2008)
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Finite energy foliations on overtwisted contact manifolds

Chris Wendl
Geometry & 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 2000
Primary: 32Q65
Secondary: 57R17
References
Publication
Received: 19 November 2006
Accepted: 20 December 2007
Published: 12 March 2008
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich and Simon Donaldson
Authors
Chris Wendl
Departement Mathematik
HG G38.1
Rämistrasse 101
8092 Zürich
Switzerland
http://www.math.ethz.ch/~wendl/