In mathematics, the symplectization (or symplectification) of a contact manifold is a symplectic manifold which naturally corresponds to it.

Definition

. Consider the set

of all nonzero 1-forms as their kernel. The union

is a symplectic submanifold of the cotangent bundle, and thus possesses a natural symplectic structure.

The projection supplies the symplectization with the structure of a principal bundle with structure group.

The coorientable case

When the contact structure is cooriented by means of a contact form are considered:

is trivial. Any section of this bundle is a coorienting form for the contact structure.