Finite energy foliations on overtwisted contact manifolds

Wendl, Chris

doi:10.2140/gt.2008.12.531

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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/

Volume 12, issue 1 (2008)