# Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(3, 1)

## TL;DR

This paper analyzes the topological structure of Liouville foliations in a Kovalevskaya integrable system on so(3,1), computing Fomenko-Zieschang invariants to classify the foliation topology.

## Contribution

It provides the first topological classification of Liouville foliations for this specific integrable case on so(3,1) using Fomenko-Zieschang invariants.

## Key findings

- Computed Fomenko-Zieschang invariants for the system
- Classified the topology of Liouville foliations on regular isoenergy surfaces
- Extended topological methods to a new Lie algebra setting

## Abstract

In this paper, we study the topology of the Liouville foliation of an analogue of the Kovalevskaya integrable case on the Lie algebra so(3; 1). The Fomenko-Zieschang invariants (i.e., marked molecules) of a given foliation on each regular isoenergy surface were calculated.