𝑘-Parabolic subspace arrangements

Barcelo, Hélène; Severs, Christopher; White, Jacob

doi:10.1090/S0002-9947-2011-05336-5

$k$-Parabolic subspace arrangements
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by Hélène Barcelo, Christopher Severs and Jacob A. White PDF

Trans. Amer. Math. Soc. 363 (2011), 6063-6083 Request permission

Abstract:

In this paper, we study $k$-parabolic arrangements, a generalization of $k$-equal arrangements for finite real reflection groups. When $k=2$, these arrangements correspond to the well-studied Coxeter arrangements. Brieskorn (1971) showed that the fundamental group of the complement, over $\mathbb {C}$, of the type $W$ Coxeter arrangement is isomorphic to the pure Artin group of type $W$. Khovanov (1996) gave an algebraic description for the fundamental group of the complement, over $\mathbb {R}$, of the $3$-equal arrangement. We generalize Khovanov’s result to obtain an algebraic description of the fundamental groups of the complements of $3$-parabolic arrangements for arbitrary finite reflection groups. Our description is a real analogue to Brieskorn’s description.

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