Topology of factored arrangements of lines
by Luis Paris PDF
A real arrangement of affine lines is a finite family $\mathcal {A}$ of lines in ${{\mathbf {R}}^2}$. A real arrangement $\mathcal {A}$ of lines is said to be factored if there exists a partition $\Pi = ({\Pi _1},{\Pi _2})$ of $\mathcal {A}$ into two disjoint subsets such that the Orlik-Solomon algebra of $\mathcal {A}$ factors according to this partition. We prove that the complement of the complexification of a factored real arrangement of lines is a $K(\pi ,1)$ space.
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