2000 character limit reached
Monodromy of stratified braid groups, II (2403.04496v2)
Published 7 Mar 2024 in math.GT and math.GR
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.
- A. Calderon and N. Salter. Framed mapping class groups and the monodromy of strata of abelian differentials. J. Eur. Math. Soc. (JEMS), 25(12):4719–4790, 2023.
- M. Dougherty and J. McCammond. Geometric combinatorics of polynomials II: the critical value complex. In preparation.
- M. Dougherty and J. McCammond. Geometric combinatorics of polynomials I: The case of a single polynomial. J. Algebra, 607(part B):106–138, 2022.
- B. Farb and D. Margalit. A primer on mapping class groups, volume 49 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 2012.
- Q. Gendron and G. Tahar. Différentielles abéliennes à singularités prescrites. J. Éc. polytech. Math., 8:1397–1428, 2021.
- Q. Gendron and G. Tahar. Isoresidual fibration and resonance arrangements. Lett. Math. Phys., 112(2):Paper No. 33, 36, 2022.
- A. Hatcher and K. Vogtmann. Tethers and homology stability for surfaces. Algebr. Geom. Topol., 17(3):1871–1916, 2017.
- M. Kontsevich and A. Zorich. Lyapunov exponents and Hodge theory. Preprint, https://arxiv.org/abs/hep-th/9701164, 1997.
- M. Kontsevich and A. Zorich. Connected components of the moduli spaces of Abelian differentials with prescribed singularities. Invent. Math., 153(3):631–678, 2003.
- E. Looijenga and G. Mondello. The fine structure of the moduli space of abelian differentials in genus 3. Geom. Dedicata, 169:109–128, 2014.
- J. McCammond. Dual braids and the braid arrangement. Preprint, https://web.math.ucsb.edu/ jon.mccammond/papers/dual-braid-arrangement-survey.pdf, 2022.
- A. Putman. A note on the connectivity of certain complexes associated to surfaces. Enseign. Math. (2), 54(3-4):287–301, 2008.
- N. Salter. Monodromy and vanishing cycles in toric surfaces. Invent. Math., 216(1):153–213, 2019.
- N. Salter. Stratified braid groups: monodromy. Preprint, https://arxiv.org/abs/2304.04627, 2023.
- Degree-d𝑑ditalic_d-invariant laminations. In What’s next?—the mathematical legacy of William P. Thurston, volume 205 of Ann. of Math. Stud., pages 259–325. Princeton Univ. Press, Princeton, NJ, 2020.
- A. Wright. Translation surfaces and their orbit closures: an introduction for a broad audience. EMS Surv. Math. Sci., 2(1):63–108, 2015.
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