Symplectic filling

Symplectic filling is a concept from the field of symplectic geometry, a branch of differential geometry. It particularly deals with the relationship between contact manifolds and symplectic manifolds. A **contact manifold** is a type of manifold equipped with a contact form, which is a differential form that gives rise to a hyperplane distribution on the manifold. The simplest example of a contact manifold is the 3-dimensional sphere with the standard contact structure.