论文标题
可超过的posets和光纤型阿贝利安安排
Supersolvable posets and fiber-type abelian arrangements
论文作者
论文摘要
我们对连接的阿贝尔谎言组的广义配置空间的纤维束进行了组合分析。这些束类似于Fadell-Neuwirth的配置空间，它们的存在是通过相关有限的部分排序集的组合属性检测到的。这与TERAO的纤维化定理连接了超平面布置捆绑包，与斯坦利的晶格超透水性连接在一起。我们获得了一个组合确定的K（$π$，1）复的和椭圆形的排列。在较强的组合条件下，当Lie群体不恰当时，我们证明了庞加莱多项式的分解。在曲曲面的情况下，这提供了Falk-Randell的公式的类似物，该公式将庞加莱多项式与基本组的下中央系列有关。
We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell-Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set. This is consistent with Terao's fibration theorem connecting bundles of hyperplane arrangements to Stanley's lattice supersolvability. We obtain a combinatorially determined class of K($π$,1) toric and elliptic arrangements. Under a stronger combinatorial condition, we prove a factorization of the Poincaré polynomial when the Lie group is noncompact. In the case of toric arrangements, this provides an analogue of Falk-Randell's formula relating the Poincaré polynomial to the lower central series of the fundamental group.
