Geometry & Topology

Finite energy foliations on overtwisted contact manifolds

Chris Wendl

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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.

Article information

Geom. Topol., Volume 12, Number 1 (2008), 531-616.

Received: 19 November 2006
Accepted: 20 December 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q65: Pseudoholomorphic curves
Secondary: 57R17: Symplectic and contact topology

holomorphic curves contact geometry finite energy foliation transverse surgery


Wendl, Chris. Finite energy foliations on overtwisted contact manifolds. Geom. Topol. 12 (2008), no. 1, 531--616. doi:10.2140/gt.2008.12.531.

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