An extension of the Bolsinov-Fomenko theorem on orbital classification of integrable Hamiltonian systems

The main result of the paper is an extension of the Bolsinov-Fomenko theore m on topological orbital classification of nondegenerate integrable Hamilto nian systems with two degrees of freedom on three-dimensional constant ener gy manifolds (1994). Namely, it is shown that their restriction that the in tegral has no critical circles with nonorientable separatrix diagrams can b e omitted. Our proof is based on an analogue of obstruction theory for cert ain types of Seifert fibrations.