Remarks on singularities of finite codimension in complex dynamical systems

Abstract

There is an interesting connection between the theory of algebraic functions and Artin’s braid theory: the space G _n of nth-degree polynomials not having multiple roots is the space K(π ,1) for the group B(n) of braids on n strands:

π₁(G _n ) = B(n), π _i (G _n ) = 0 for i > 1. (1)

This connection can be used in both directions: both for the study of braid groups and for the study of algebraic functions. Here are some examples.