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arXiv · 0909.0720

$k$-Parabolic Subspace Arrangements

Hélène Barcelo·Christopher Severs·Jacob A. White
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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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Hélène Barcelo, Christopher Severs, Jacob A. White. 2009-09-03. $k$-Parabolic Subspace Arrangements. https://arxiv.org/abs/0909.0720

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