Fundamental Group of complex hipocicloides

Erich Ulises Calatan (IMUNAM-Cuernavaca)

Abstract

(The talk will be in Spanish: see original abstract)

A hypocycloid can be described as the path followed by a point located on a circle of radius r that rolls inside another circle of radius s. Under the assumption that r/s is a rational number, hypocycloids are a special case of flat algebraic curves. The most studied topological invariant on these curves is the fundamental group due to its relationship with nodes and links, in particular the most used technique to calculate a presentation of the fundamental group is the Zariski Van-Kampen method. In different articles, José Ignacio Cogolludo Agustin and Enrique Artal Bartolo have calculated part of the topology of these curves, including their singularities and, in some cases, their fundamental group. The goal of this talk is to introduce the Zariski Van-Kampen technique and give some partial answers about the fundamental group of complex hypocycloids.

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