Shellable Complexes and Topology of Diagonal Arrangements |
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Authors: | Sangwook Kim |
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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 |
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Abstract: | We prove that if a simplicial complex Δ is shellable, then the intersection lattice L
Δ for the corresponding diagonal arrangement
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
where the complement
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. |
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Keywords: | Shellable simplicial complexes Diagonal arrangements K(π 1) |
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