Geometry & Topology

Finite energy foliations on overtwisted contact manifolds

Chris Wendl

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

Permanent link to this document
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

Keywords
holomorphic curves contact geometry finite energy foliation transverse surgery

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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