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

## TL;DR

This paper analyzes the topology of Liouville foliations in the Kovalevskaya integrable case on so(4), computing invariants and describing parameter stratification to classify the foliations.

## Contribution

It provides the first detailed calculation of Fomenko-Zieschang invariants for this specific integrable system on so(4).

## Key findings

- Computed Fomenko-Zieschang invariants for the foliations.
- Described the stratification of parameter space.
- Classified Liouville foliations for the Kovalevskaya case on so(4).

## Abstract

Topology of Liouville foliations for an analogue of the Kovalevskaya integrable case on Lie algebra so(4) is discussed. Fomenko-Zieschang invariants (i.e. marked molecules) were calculated for these foliations on every regular isoenergy submanifold. The corresponding stratification of the three-dimensional space of parameters of these manifolds is described in details.