Pseudoholomorphic Cylinders in Symplectisations

Properties of Pseudoholomorphic Curves in Symplectisations I: Asymptotics

Properties of Pseudoholomorphic Curves in Symplectisations Iv: Asymptotics with Degeneracies

We study pseudoholomorphic maps ~ u = (a; u): _ S ! R M de-ned on punctured Riemannian surfaces, satisfying T ~ u i = ~ J T ~ u, with a special almost complex structure ~ J associated with a contact form on the 3-dimensional compact manifold M. If the energy of ~ u is bounded, the projection u into M tends, as jzj ! 1, to a periodic orbit x(t) of the Reeb vector eld X deened by. We describe the...

Gluing Pseudoholomorphic Curves along Branched Covered Cylinders I 1 Statement of the Gluing Theorem 1.1 Pseudoholomorphic Curves in Symplectizations

This paper and its sequel prove a generalization of the usual gluing theorem for two index 1 pseudoholomorphic curves u+ and u− in the symplectization of a contact 3-manifold. We assume that for each embedded Reeb orbit γ, the total multiplicity of the negative ends of u+ at covers of γ agrees with the total multiplicity of the positive ends of u− at covers of γ. However, unlike in the usual gl...

Gluing pseudoholomorphic curves along branched covered cylinders II

This paper and its prequel (“Part I”) prove a generalization of the usual gluing theorem for two index 1 pseudoholomorphic curves U+ and U− in the symplectization of a contact 3-manifold. We assume that for each embedded Reeb orbit γ, the total multiplicity of the negative ends of U+ at covers of γ agrees with the total multiplicity of the positive ends of U− at covers of γ. However, unlike in ...

A compendium of pseudoholomorphic beasts in R ( S 1 S 2 )

This article describes various moduli spaces of pseudoholomorphic curves on the symplectization of a particular overtwisted contact structure on S1 S2 . This contact structure appears when one considers a closed self dual form on a 4{ manifold as a symplectic form on the complement of its zero locus. The article is focussed mainly on disks, cylinders and three-holed spheres, but it also supplie...