Monodromy of stratified braid groups, II
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916354831941632 |
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| author | Salter, Nick |
| author_facet | Salter, Nick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monodromy of stratified braid groups, II Salter, Nick Geometric Topology Group Theory 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. |
| title | Monodromy of stratified braid groups, II |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2403.04496 |