The cohomology rings of complements of subspace arrangements
The cohomology rings of complements of subspace arrangements
复制标题
子空间排列补集的上同调环
DOI：
10.1007/pl00004452
复制
发表时间：
2001
影响因子：
1.4
通讯作者：
Carsten Schultz
中科院分区：
文献类型：
--
作者：
Mark de Longueville;Carsten Schultz
抽象的。考虑了真实的线性子空间排列的补的积分上同调的环结构。Goresky和MacPherson的一个定理用交偏序集和维数函数给出了上同调的加法结构，而对于余维数为1的无交排列，我们用交偏序集、维数函数和参与子空间的方向描述了乘法结构.特别是，这产生了一个描述的积分上同调环的复杂安排prostretured由Yuzvinsky。对于一般的真实的排列，得到了一个较弱的结果.方法是几何的，方法是基本的。
Abstract. The ring structure of the integral cohomology of complements of real linear subspace arrangements is considered. While the additive structure of the cohomology is given in terms of the intersection poset and dimension function by a theorem of Goresky and MacPherson, we describe the multiplicative structure in terms of the intersection poset, the dimension function and orientations of the participating subspaces for the class of arrangements without pairs of intersections of codimension one. In particular, this yields a description of the integral cohomology ring of complex arrangements conjectured by Yuzvinsky. For general real arrangements a weaker result is obtained. The approach is geometric and the methods are elementary.