Boundary manifolds of line arrangements

While the boundary 3-manifold of a line arrangement in the complex plane de pends only on the incidence correspondence of the line arrangement, the hom otopy type of the complement depends on the relative positions of incidence s. In this paper we describe the homotopy type of line arrangement compleme nts in terms of an associated plumbed graph. For pseudo-real line arrangeme nts this method provides an explicit description of the homotopy type and f undamental group of the complement in terms of its ordered incidence graph. The method also extends to a larger class of "unknotted" line arrangements .