Helene Barcelo: r-Disjoint k-Parabolic Subspace Arrangements

Abstract

r-disjoint k-parabolic subspace arrangements are a natural generalization of the well-studied k-equal arrangements of type A, B and D. Using discrete homotopy theory techniques we obtain an algebraic description of the fundamental group of the complement of these subspace arrangements when k = 3, r = 1. We also discuss a polyhedral complex that has the same homotopy type as the complement of these subspaces allowing us to compute all homotopy groups for all k and r. This is joint work with Chris Severs and Jacob White