Year: 2024
Type: article
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 $$\mathbb{C}\mathbb{P}^1$$ C P 1 induced by the logarithmic derivative $$\textrm{d}f/f$$ d f / f of a polynomial in the stratum.
Author: Nick Salter
Institution: University of Notre Dame
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
OpenAlex ID: W4403275941