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Intersection of Parabolic Subgroups in Euclidean Braid Groups: a short proof (2402.10919v1)
Published 24 Jan 2024 in math.GR
Abstract: We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group $A[B{n+1}]$ is isomorphic to $A[\tilde{A}_n] \rtimes \mathbb{Z}$.
- The K(π,1)𝐾𝜋1K(\pi,1)italic_K ( italic_π , 1 )-Problem for Hyperplane Complements Associated to Infinite Reflection Groups. J. Amer. Math. Soc., 8(3), 597–627.
- Cohomology of Coxeter groups and Artin groups. Mathematical Research Letters, 7(03), 213–232.
- On parabolic subgroups of Artin–Tits groups of spherical type. Adv. Math., 352, 572 – 610.
- Parabolic subgroups of large-type Artin groups. Mathematical Proceedings of the Cambridge Philosophical Society, 174(2), 393–414.
- Haettel, Thomas. 2021. Lattices, injective metrics and the K(π,1)𝐾𝜋1K(\pi,1)italic_K ( italic_π , 1 ) conjecture. Algebraic & Geometric Topology (to appear). arXiv:2109.07891.
- A Geometric and Algebraic Description of Annular Braid Groups. IJAC, 12(02), 85–97.
- Paris, Luis. 2014. K(π,1)𝐾𝜋1K(\pi,1)italic_K ( italic_π , 1 ) conjecture for Artin groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Ser. 6, 23(2), 361–415.
- Van der Lek, Harm. 1983. The Homotopy Type of Complex Hyperplane Complements. Ph.D. thesis, Nijmegen.
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