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 theorem on topological orbital classification of nondegenerate integrable Hamiltonian systems with two degrees of freedom on three-dimensional constant energy manifolds (1994). Namely, it is shown that their restriction that the integral has no critical circles with nonorientable separatrix diagrams can be omitted. Our proof is based on an analogue of obstruction theory for certain types of Seifert fibrations.