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arXiv · 2403.04496

Monodromy of stratified braid groups, II

Nick Salter
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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.

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Nick Salter. 2024-08-12. Monodromy of stratified braid groups, II. https://arxiv.org/abs/2403.04496

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