Real algebraic knots and links of small degree

TL;DR

This paper classifies real algebraic knots and links of degree up to six and genus up to one in real projective 3-space, providing topological and rigid isotopy classifications.

Contribution

It offers the first comprehensive classification of small-degree real algebraic knots and links, combining topological and rigid isotopy perspectives.

Findings

Complete classification of algebraic knots and links of degree ≤ 6

Identification of topological types for genus ≤ 1 curves

Distinction between topological and rigid isotopy classes

Abstract

The paper gives topological as well as rigid isotopy classification of smooth irreducible algebraic curves in the real projective 3-space for the case when the degree of the curve is at most six and its genus is at most one.