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Shellable Complexes and Topology of Diagonal Arrangements
Authors:Sangwook Kim
Institution:(1) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;(2) Present address: Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
Abstract: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. This work forms part of the author’s doctoral dissertation at the University of Minnesota, supervised by Vic Reiner, and partially supported by NSF grant DMS-0245379.
Keywords:Shellable simplicial complexes  Diagonal arrangements            K(π    1)
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