Combinatorics of Orbit Configuration Spaces
Combinatorics of Orbit Configuration Spaces
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轨道配置空间的组合学
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Nir Gadish
中科院分区：
文献类型：
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作者：
C. Bibby;Nir Gadish
从空间上的一个群体动作出发，通过坚持没有两个点位于同一轨道上来定义配置空间的一个变体。当作用量几乎为自由时，这个“轨道构形空间”是笛卡尔积内部一系列子簇的补充，我们利用这种结构来研究它的拓扑结构。我们给出了它的层的偏序集(交集的连通分支)的抽象组合描述，作为划分和Dowling格的推广，它具有很强的独立性。然后利用与这些经典偏序集的密切关系来给出显式上同调计算。
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this “orbit configuration space” is the complement of an arrangement of subvarieties inside the Cartesian product, and we use this structure to study its topology. We give an abstract combinatorial description of its poset of layers (connected components of intersections from the arrangement), which turns out to be of much independent interest as a generalization of partition and Dowling lattices. The close relationship to these classical posets is then exploited to give explicit cohomological calculations.