发表机构
Louisiana State University（路易斯安那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造了局部几何偏序集的Orlik–Solomon代数，利用其与复阿贝尔李群子群排列的关联，结合拓扑信息计算排列补集的有理上同调，尤其给出紧李群情形下的显式微分分次代数。
AI 中文摘要
我们为任意局部几何偏序集构造Orlik–Solomon代数，作为几何格对应的Orlik–Solomon代数的自然推广。该代数具有若干有趣性质，包括通过Gröbner基理论得到的组合型无破圈向量空间基。当偏序集刻画复阿贝尔李群中某类子群排列的相交数据时，我们为Orlik–Solomon代数注入拓扑信息，以计算排列补集的有理上同调。特别地，当李群为紧群时，我们给出一个显式微分分次代数，其上同调即为该排列补集的有理上同调。
英文摘要
We construct an Orlik--Solomon algebra for any locally geometric poset as a natural generalization of the one for geometric lattices. This algebra has several interesting features, including a combinatorial no-broken-circuit basis that we obtain through Gröbner basis theory. When the poset captures the intersection data of an arrangement of certain subgroups in a complex abelian Lie group, we infuse the Orlik--Solomon algebra with topological information to compute the cohomology of the arrangement complement. In particular, when the Lie group is compact, we present an explicit differential graded algebra whose cohomology is the rational cohomology of the arrangement complement. We further exhibit a family of abelian arrangements whose integer cohomology has torsion.
Commentsv1. 27 pages; v2. 28 pages, extended to integer coefficients
