A contact geometric proof of the Whitney-Graustein theorem

TL;DR

This paper provides a straightforward proof of the Whitney-Graustein theorem, which classifies regular closed curves in the plane by their rotation number, using contact geometry techniques.

Contribution

It introduces a novel contact geometric approach to prove the Whitney-Graustein theorem, simplifying the understanding of curve classification.

Findings

Proof based on contact geometry simplifies the classification process.

Establishes a new geometric perspective on the theorem.

Enhances understanding of regular homotopy in planar curves.

Abstract

The Whitney-Graustein theorem states that regular closed curves in the 2-plane are classified, up to regular homotopy, by their rotation number. Here we give a simple proof based on contact geometry.