Boundary manifolds of line arrangements

Abstract. While the boundary 3-manifold of a line arrangement in the complex plane depends only on the incidence correspondence of the line arrangement, the homotopy type of the complement depends on the relative positions of incidences. In this paper we describe the homotopy type of line arrangement complements in terms of an associated plumbed graph. For pseudo-real line arrangements this method provides an explicit description of the homotopy type and fundamental group of the complement in terms of its ordered incidence graph. The method also extends to a larger class of “unknotted” line arrangements.