Maximally writhed real algebraic links

TL;DR

This paper classifies real algebraic links in projective space that maximize a specific rigid isotopy invariant, providing a detailed understanding of their structure and properties.

Contribution

It introduces a classification of degree d real algebraic links with maximal invariant values, expanding the understanding of their geometric and topological features.

Findings

Classification of maximal invariant real algebraic links

Identification of properties distinguishing these links

Extension of Viro's invariant to broader link types

Abstract

Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots and links in $\Bbb{RP}^3$ which can be viewed as a first order Vassiliev invariant. In this paper we classify real algebraic links of degree $d$ with the maximal value of this invariant in its two versions: $w$ and $w_\lambda$.