2024/03/07 by Nick Salter, Salter, Nick
Mathematics · #Geometric and Algebraic Topology #Advanced Algebra and Geometry #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2403.04496
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 \mathbbCP1 induced by the logarithmic derivative df/f of a polynomial in the stratum.