2. Suspension. Let be a group action on a manifold . Then we consider the induced action of on the product manifold , where . Consider the quotient space , on which there is a natural action that comes from shift . Clearly the later commutes with the action and desends to an action on .
1. Let be a symplectic manifold, be a nonsingular symplectic vector field in the sense that . Then is a primitive of , and hence is an exact symplectic manifold.