%0 Journal Article
%T $k$-Parabolic Subspace Arrangements
%A H¨¦l¨¨ne Barcelo
%A Christopher Severs
%A Jacob A. White
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0909.0720v1