Geometry & Topology

Finite energy foliations on overtwisted contact manifolds

Chris Wendl

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.

Article information

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

Dates
Accepted: 20 December 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800027

Digital Object Identifier
doi:10.2140/gt.2008.12.531

Mathematical Reviews number (MathSciNet)
MR2390353

Zentralblatt MATH identifier
1141.53082

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

Citation

Wendl, Chris. Finite energy foliations on overtwisted contact manifolds. Geom. Topol. 12 (2008), no. 1, 531--616. doi:10.2140/gt.2008.12.531. https://projecteuclid.org/euclid.gt/1513800027

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