Complex symplectic structures and the $$\partial {\bar{\partial }}$$ ∂ ∂ ¯ -lemma

Complex structures on 4-manifolds with symplectic 2-torus actions

We apply the general theory for symplectic torus actions with symplectic or coisotropic orbits to prove that a 4-manifold with a symplectic 2-torus action admits an invariant complex structure and give an identification of those that do not admit a Kähler structure with Kodaira’s class of complex surfaces which admit a nowhere vanishing holomorphic (2, 0)-form, but are not a torus or a K3 surface.

Cocycles, Symplectic Structures and Intersection

Uniqueness of Symplectic Structures

This survey paper discusses some uniqueness questions for symplectic forms on compact manifolds without boundary.

Diffuse scattering and partial disorder in complex structures

The study of single-crystal diffuse scattering (SCDS) goes back almost to the beginnings of X-ray crystallography. Because SCDS arises from two-body correlations, it contains information about local (short-range) ordering in the sample, information which is often crucial in the attempt to relate structure to function. This review discusses the state of the field, including detectors and data co...

Symplectic realizations of bihamiltonian structures

A smooth manifold M is endowed by a Poisson pair if two linearly independent bivectors c1, c2 are defined on M and moreover cλ = λ1c1+ λ2c2 is a Poisson bivector for any λ = (λ1, λ2) ∈ R 2. A bihamiltonian structure J = {cλ} is the whole 2-dimensional family of bivectors. The structure J (the pair (c1, c2)) is degenerate if rank cλ < dim M,λ ∈ R 2. The degenerate bihamiltonian structures play i...