Discrete curves in CP1 and the Toda lattice

TL;DR

This paper explores flows on discrete curves in complex projective and complex spaces, offering a new interpretation of the Toda lattice hierarchy as flows on these curves, linking integrable systems with geometric structures.

Contribution

It introduces a novel geometric interpretation of the Toda lattice hierarchy as flows on discrete curves in complex spaces, connecting integrable systems with discrete differential geometry.

Findings

New interpretation of Toda lattice hierarchy as flows on discrete curves

Establishment of connections between integrable systems and discrete geometry

Framework for analyzing discrete curves in complex projective and complex spaces

Abstract

In this paper we investigate flows on discrete curves in $\C^2$, $\CP^1$, and $\C$. A novel interpretation of the one dimensional Toda lattice hierarchy and reductions thereof as flows on discrete curves will be given.