On W_3-morphisms and the Geometry of Plane Curves

TL;DR

This paper explores the geometric interpretation of W_3-morphisms through deformations of convex plane curves, offering insights into their structure and potential extensions to higher dimensions and more complex curves.

Contribution

It provides a geometric description of W_3 transformations via convex curve deformations and discusses extensions to W_n and higher-dimensional curved spaces.

Findings

W_3-morphisms can be understood through convex curve deformations

The approach offers a new perspective on finite W_3-morphisms

Potential for extending the geometric interpretation to W_n and higher dimensions

Abstract

We provide a description of W_3 transformations in terms of deformations of convex curves in two dimensional Euclidean space. This geometrical interpretation sheds some light on the nature of finite W_3-morphisms. We also comment on how this construction can be extended to the case of W_n and ``nicely curved'' curves in $\reals^{n-1}$.