Real algebraic realizations of divide links

• Grant number: 24/20882-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Raimundo Nonato Araújo dos Santos
• Grantee: Arthur Garcia Tonus
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

A'Campo introduced the family of divide links and showed that all (complex) algebraic links are divide links, and all divide links are fibered. As it is well known, however, that not all fibered links aredivide links, for instance, the figure-eight knot is not a dividelink. It is not known yet how big the set of divide links is inside the set of fibered links. On the other hand, the Benedetti-Shiota conjecture states that a link is real algebraic if and only if it isfibered. This project aims to prove that every divide link is real algebraic, thereby giving further evidence forthe Benedetti-Shiota conjecture.