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In this paper we study topological properties of an integrable case forEuler's equations on the Lie algebra $\textrm{so}(4)$, which can be regarded asan analogue of the classical Kovalevskaya case in rigid body dynamics. Inparticular, for all values of the parameters of the system under considerationthe bifurcation diagrams of the momentum mapping are constructed, the types ofcritical points of rank $0$ are determined, the bifurcations of Liouville toriare described and the loop molecules for all singular points of the bifurcationdiagram are computed. It follows from the obtained results that sometopological properties of the classical Kovalevskaya case can be obtained fromthe corresponding properties of the considered integrable case on the Liealgebra $\textrm{so}(4)$ by taking a natural limit.

The topology of Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)