Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(4)

This paper is concerned with the topology of the Liouville foliation in the analogue of the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$. The Fomenko-Zieschang invariants (that is, marked molecules) for this foliation are calculated on each nonsingular iso-energy surface. A detailed description of the resulting stratification of the three- dimensional space of parameters of the iso-energy surfaces is given.