Fonctionne avec Indico
v3.2.9
Given the equation of a complex isolated hypersurface singularity, the associated universal unfolding space contains the discriminant of perturbed equations with a singular zero level set. The fundamental group of its complement is called the discriminant knot group of the singularity. The most prominent examples are the braid group and more general the Artin groups of types ADE, which arise for the singularity types of the same name. I will review an older result which provides a finite presentation of the discriminant knot group in the case of plane Brieskorn-Pham singularities, and a new result with Sebastian Baader, that involves the same presentations in a more general knot-theoretic setting. On both sides the braid group plays a distinctive role, on one side through the notion of braid monodromy, on the other by properties of the monoid of positive braids.