Some tight contact foliations can be approximated by overtwisted ones

Finite Energy Foliations on Overtwisted Contact Manifolds

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 ...

What Can Be Approximated by Polynomials with Integer Coefficients

Can billiard eigenstates be approximated by superpositions of plane waves ?

The plane wave decomposition method (PWDM) is one of the most popular strategies for numerical solution of the quantum billiard problem. The method is based on the assumption that each eigenstate in a billiard can be approximated by a superposition of plane waves at a given energy. By the classical results on the theory of differential operators this can indeed be justified for billiards in con...

Legendrian Ribbons in Overtwisted Contact Structures

We show that a null–homologous transverse knot K in the complement of an overtwisted disk in a contact 3–manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self–linking number of K with respect to S satisfies sl(K,S) = −χ(S). In particular, every null–homologous topological knot type in an overtwisted contact manifold can be represented...

Foliations and contact structures

We introduce a notion of linear deformation of codimension one foliations into contact structures and describe some foliations which deform instantly into contact structures and some which do not. Restricting ourselves to closed smooth manifolds, we obtain a necessary and su‰cient condition for a foliation defined by a closed nonsingular 1-form to be linearly deformable into contact structures....