A short proof that equisingular branches are isotopic

TL;DR

This paper provides a concise proof that equisingular irreducible plane analytic curve germs are isotopic, avoiding the need to analyze the knot structures associated with these germs.

Contribution

It offers a simplified proof establishing isotopy of equisingular plane curve germs without relying on knot theory.

Findings

Equisingular germs are isotopic.

Simplified proof avoids knot theory.

Enhances understanding of plane curve singularities.

Abstract

We present a short proof of the fact that two irreducible germs of plane analytic curves are isotopic if they are equisingular, without recourse to the structure of the associated knots.