On real algebraic links in the 3-sphere associated with mixed polynomials

TL;DR

This paper introduces new classes of mixed singularities that realize real algebraic links in the 3-sphere, potentially advancing understanding of the classification of such links and related conjectures.

Contribution

It constructs novel mixed singularities that realize real algebraic links, offering new tools for studying their classification and properties.

Findings

New classes of mixed singularities constructed

Real algebraic links realized in the 3-sphere

Potential implications for the Benedetti-Shiota conjecture

Abstract

In this paper we construct new classes of mixed singularities that provide realizations of real algebraic links in the $3$-sphere. Classifications and characterizations of real algebraic links are still open. These new classes of mixed singularities may help to shed light on the Benedetti-Shiota conjecture, which state that any fibered link on the $3$-sphere is a real algebraic link.