Homotopy types of subspace arrangements via diagrams of spaces
Homotopy types of subspace arrangements via diagrams of spaces
复制标题
通过空间图的子空间排列的同伦类型
DOI：
10.1007/bf01444901
复制
发表时间：
1993
影响因子：
1.4
通讯作者：
R. Živaljević
中科院分区：
文献类型：
--
作者：
G. Ziegler;R. Živaljević
我们证明了（仿射，压缩仿射，球形或投影）子空间布置的子空间联合的同型类型的组合公式。从这些公式中，我们得出了Goresky＆MacPherson关于安排同源及其补体同源的结果。布置的结合可以解释为交叉路口上空间图的直接极限。通过获取此图的同置直接限制，获得了密切相关的空间。我们的方法包括在同一POSET上构造组合模型图，该图可以通过通常的同件比较空间图将其与原始的限制进行比较。
We prove combinatorial formulas for the homotopy type of the union of the subspaces in an (affine, compactified affine, spherical or projective) subspace arrangement. From these formulas we derive results of Goresky & MacPherson on the homology of the arrangement and the cohomology of its complement. The union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset. A closely related space is obtained by taking the homotopy direct limit of this diagram. Our method consists in constructing a combinatorial model diagram over the same poset, whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces.