The mondromy of the Lagrange Top and the Picard-Lefschetz formula

TL;DR

This paper demonstrates how the monodromy of action variables in the Lagrange top and similar systems can be derived from the monodromy of cycles on hyperelliptic curves using the Picard-Lefschetz formula.

Contribution

It connects the monodromy of classical integrable systems with the Picard-Lefschetz theory of hyperelliptic curves, providing a geometric method to compute monodromy.

Findings

Monodromy of the Lagrange top relates to hyperelliptic curve cycles.

Picard-Lefschetz formula computes monodromy of cycles.

Method applies to generalizations of the Lagrange top.

Abstract

The purpose of this paper is to show that the monodromy of action variables of the Lagrange top and its generalizations can be deduced from the monodromy of cycles on a suitable hyperelliptic curve (computed by the Picard-Lefschetz formula).