Monodromy of stratified braid groups, II

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 com...

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Bibliographic Details
Main Author Salter, Nick
Format Journal Article
LanguageEnglish
Published 07.03.2024
Subjects
Mathematics - Geometric Topology
Mathematics - Group Theory
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Summary: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.
DOI:10.48550/arxiv.2403.04496