Suspensions of affine arrangements
Suspensions of affine arrangements
复制标题
仿射排列的中止
DOI：
10.1007/s002080050121
复制
发表时间：
1997
影响因子：
1.4
通讯作者：
C. Schaper
中科院分区：
文献类型：
--
作者：
C. Schaper
已知仿射排列的补的同调型甚至稳定同伦型都是由组合数据决定的。各种有趣的空间（例如纯辫子群的K（π，1）-空间）都具有这种排列补的结构。这一结果产生，如果一个安排的补充和暂停它“经常足够”，一个空间的同伦类型只依赖于偏序集的交叉连同维数函数。例如，在复杂超平面排列的情况下，这个空间是各种维度的球体的有限楔形。这让人不禁要问，到底需要多少个暂停。在本文中，我们表明，从Spanier-Whitehead对偶得到明确的上限的暂停数。以这种方式获得的界限是相对较弱的，本文件的困难的部分是要表明，在仿射安排的特定情况下，更好的结果是真实的：特别是，在复杂的安排的情况下，一个单一的悬挂确实足够。
It is known that the homology type and even the stable homotopy type of the complement of an affine arrangement is determined by combinatorial data. Various interesting spaces (eg the K (π, 1)-spaces of the pure braid group) have the structure of such arrangement complements. This result yields that if one takes the complement of an arrangement and suspends it “often enough”, one obtains a space whose homotopy type depends only on the poset of intersections together with the dimension function. For example in the case of complex hyperplane arrangements this space is a finite wedge of spheres of various dimensions. This leads one to ask how many suspensions are needed. In this paper we show that from Spanier-Whitehead duality one gets explicit upper bounds for the number of suspensions. The bounds obtained in this way are relatively weak, and the harder part of the present paper is to show, that in the specific situation of affine arrangements much better results are true: in particular, in the case of complex arrangements one single suspension does suffice.