On completely integrable systems with local torus actions (Q1381946)

The subject of the paper is the symplectic topology of completely integrable Hamiltonian dynamical systems with a compact phase space. The considered class of systems is defined by the condition that they may have only nondegenerate elliptic singularities. The paper presents a description of all such systems whose universal covering admits introduction of a corresponding set of action-angle variables. It is proved that some finite cover of the system is diffeomorphic to a product of a so-called convex polytope and a solvmanifold. These results generalize, for integrable systems with several degrees of freedom, a theorem proved earlier by Fomenko and Bolsinov for integrable systems with two degrees of freedom.