Shellable complexes and topology of diagonal arrangements

Abstract

We prove that if a simplicial complex Δ is shellable, then the intersection lattice L Δ for the corresponding diagonal arrangement AΔ is homotopy equivalent to a wedge of spheres. Furthermore, we describe precisely the spheres in the wedge, based on the data of shelling. Also, we give some examples of diagonal arrangements A where the complement MA is K(π,1), coming from rank-3 matroids. © 2008 Springer Science+Business Media, LLC.