Finite Energy Foliations on Overtwisted Contact Manifolds

Details Finite Energy Foliations on Overtwisted Contact Manifolds Finite Energy Foliations on Overtwisted Contact Manifolds

2006-11-17

arxiv.org/abs/math/0611516v2

Geometry & Topology 12 (2008) 531-616

Mathematics

Symplectic Geometry

76 pages, 15 figures; typos corrected

Scientific paper

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.

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