Real $K(\pi,1)$ arrangements from finite root systems

Consider the arrangement of codimension two subspaces of an $n$-dimensional Euclidean space ${\Bbb R}^n=\lbrace (x_1,...,x_n)|x_i\in {\Bbb R}\rbrace$, that consists of triple diagonals $x_i=x_j=x_k$ for all $1\le i<j<k\le n.$ We answer positively A.Björner’s question whether the complement of this arrangement is a $K(\pi,1)$ space. We construct some other $K(\pi,1)$ arrangements and show that they come naturally from finite root systems.

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Published 1 January 1996