Topological classification of the Goryachev integrable case in rigid body dynamics (Q2812511)

\textit{A. T. Fomenko} and \textit{H. Zieschang} [Math. USSR, Izv. 36, No. 3, 567--596 (1991); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 3, 546--575 (1990; Zbl 0723.58024)] proved that \textit{two integrable systems on nonsingular \(3\)-dimensional compact connected isoenergy surfaces are Liouville equivalent if and only if they have the same marked molecules}. Based on this result, the author characterized topologically the Goryachev integrable case in rigid body dynamics by presenting the marked molecules for the four zones of regular values of the energy. These marked molecules are topological invariants and give a complete description of the systems in Goryachev case on various level sets of the energy.