Graph-manifolds and integrable Hamiltonian systems

We study the topology of the three-dimensional constant- energy manifolds of integrable Hamiltonian systems realizable in the form of a special class of so-called `molecules'. Namely, for this class of manifolds the Reidemeister torsion is calculated in terms of the Fomenko-Zieschang invariants. A connection between the torsion of a constant-energy manifold and stable periodic trajectories is found. Bibliography: 17 titles.