Moser’s theorem

Let ${\omega }_0$ and ${\omega }_1$ be symplectic structures on a compact manifold $M$. If there is a pathin the space of symplectic structures of a fixed DeRham cohomology class connecting ${\omega }_0$ and ${\omega }_1$ (in particular ${\omega }_0$ and ${\omega }_1$ must have the same class),then $(M,{\omega }_0)$ and $(M,{\omega }_1)$ are symplectomorphic, by a symplectomorphismisotopic to the identity.