On the homology of the real complement of the k-parabolic subspace arrangement

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• 作者：Christopher Severs^a ; ^{chris.severs@gmail.com} ; Jacob A. White^b ; ¹ ; ^{jawhite@msri.org}
• 关键词：Subspace arrangements ; Coxeter groups ; Discrete Morse theory
• 刊名：Journal of Combinatorial Theory ; Series A
• 出版年：2012
• 期刊代码：72_00973165
• 类别：mt
• 出版时间：August, 2012
• 卷：119
• 期：6
• 页码：1336-1350
• 文件大小：279 K

摘要

In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When , these arrangements correspond to the well-studied Coxeter arrangements. We construct a cell complex that is homotopy equivalent to the complement. We then apply discrete Morse theory to obtain a minimal cell complex for the complement. As a result, we give combinatorial interpretations for the Betti numbers, and show that the homology groups are torsion-free. We also study a generalization of the Independence Complex of a graph, and show that this generalization is shellable when the graph is a forest. This result is used in studying using discrete Morse theory.