# Shellable Complexes and Topology of Diagonal Arrangements

Discrete & Computational Geometry, Apr 2008

We prove that if a simplicial complex Δ is shellable, then the intersection lattice L Δ for the corresponding diagonal arrangement $\mathcal{A}_{\Delta }$ 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  $\mathcal{A}$ where the complement $\mathcal{M}_{\mathcal{A}}$ is K(π,1), coming from rank-3 matroids.

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Sangwook Kim. Shellable Complexes and Topology of Diagonal Arrangements, Discrete & Computational Geometry, 2008, 190-213, DOI: 10.1007/s00454-008-9074-x