Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups
Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups
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线路安排的最小分层和基本组的积极同质呈现
DOI：
10.1007/978-88-7642-431-1_22
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Yoshinaga
中科院分区：
文献类型：
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作者：
M. Yoshinaga
已知复超平面排列的补与极小CW复形同伦。有几种方法可以达到最小值。在本文中，我们将注意力限制在真实的二维情形，并引入了所谓的最小分层的“对偶”对象。地层被明确地描述为半代数集。分层诱导的补充划分成一个不相交的联合的可收缩空间，这是最小的意义上的余维kpieces的数量等于第k个Betti数。我们还讨论了表示的基本群与最小分层。特别是，我们证明了一个真实的安排的补充的基本群体有积极的齐次介绍。
The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the “dual” objects so called minimal stratifications. The strata are explicitly described as semialgebraic sets. The stratification induces a partition of the complement into a disjoint union of contractible spaces, which is minimal in the sense that the number of codimensionkpieces equals the k-th Betti number.We also discuss presentations for the fundamental group associated to the minimal stratification. In particular, we show that the fundamental groups of complements of a real arrangements have positive homogeneous presentations.