Hamiltonian torus actions as integrable systems For a symplectic manifold of dimension , there is a 1-1 relationship between free, locally free, or effective Hamiltonian actions and completely integrable systems. Missing \begin{Bmatrix} or extra \end{Bmatrix}\text{Hamiltonian torus actions} \end{Bmatrix} \leftrightarrow \{\text{Completely integrable systems}\} $$