# Moser’s theorem

Let $\omega_{0}$ and $\omega_{1}$ be symplectic structures on a compact manifold $M$. If there is a path in 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 symplectomorphism isotopic to the identity.

Title Moser’s theorem MosersTheorem 2013-03-22 13:18:08 2013-03-22 13:18:08 bwebste (988) bwebste (988) 6 bwebste (988) Theorem msc 53D05