# Rigid isotopy of maximally writhed links

## TL;DR

This paper proves that all maximally writhed algebraic links of the same topological type in real projective 3-space are rigidly isotopic, meaning they can be smoothly deformed into each other while preserving algebraic properties.

## Contribution

It establishes the rigidity of maximally writhed algebraic links, showing they form a single isotopy class within each topological type.

## Key findings

- Maximally writhed links of the same topological type are rigidly isotopic.
- Provides a classification of these links up to smooth deformation.
- Extends previous topological classification to algebraic isotopy.

## Abstract

This is a sequel to the paper \cite{MO-mw} which identified maximally writhed algebraic links in $\rp^3$ and classified them topologically. In this paper we prove that all maximally writhed links of the same topological type are rigidly isotopic, i.e. one can be deformed into another with a family of smooth real algebraic links of the same degree.