Geodesic
The topology of integral submanifolds of completely integrable Hamiltonian systems
Sbornik. Mathematics, Tome 62 (1989) no. 2, pp. 373-383

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It is proved that the class $(X)$ of three-dimensional closed compact manifolds that are constant energy surfaces of integrable (by means of a Bott integral) Hamiltonian systems coincides precisely with the class $(Q)$ of three-dimensional orientable manifolds admitting decomposition into “circular handles”. Fomenko previously proved the inclusion $(X)\subset(Q)$. An explicit geometric description is also given for modifications of Liouville tori in neighborhoods of nonorientable critical submanifolds of the moment mapping of an integrable system. Figures: 1. Bibliography: 20 titles. 
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     author = {A. V. Brailov and A. T. Fomenko},
     title = {The topology of integral submanifolds of completely integrable {Hamiltonian} systems},
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     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_2_a3/}
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A. V. Brailov; A. T. Fomenko. The topology of integral submanifolds of completely integrable Hamiltonian systems. Sbornik. Mathematics, Tome 62 (1989) no. 2, pp. 373-383. http://geodesic.mathdoc.fr/item/SM_1989_62_2_a3/