Monodromy of stratified braid groups, II

Abstract

The space of monic squarefree polynomials has a stratification according to the multiplicities of the critical points, called the equicritical stratification. Tracking the positions of roots and critical points, there is a map from the fundamental group of a stratum into a braid group. We give a complete determination of this map. It turns out to be characterized by the geometry of the translation surface structure on ${\mathbb{CP}}^1$ induced by the logarithmic derivative $df/f$ of a polynomial in the stratum.

New version incorporates comments from referees. Section 4 has been substantially expanded, and figures have been re-colored