Equivariant cohomology and the Varchenko-Gelfand filtration

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• 作者：Daniel Moseley ^{dmosele@ju.edu}
• 关键词：Hyperplane arrangements ; Equivariant cohomology ; Representation theory ; Configuration space ; Oriented matroids
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：472
• 期：Complete
• 页码：95-114
• 全文大小：408 K
• 卷排序：472

文摘

The cohomology of the configuration space of n   points in R3R3 is isomorphic to the regular representation of the symmetric group, which acts by permuting the points. We give a new proof of this fact by showing that the cohomology ring is canonically isomorphic to the associated graded of the Varchenko–Gelfand filtration on the cohomology of the configuration space of n   points in R1R1. Along the way, we give a presentation of the equivariant cohomology ring of the R3R3 configuration space with respect to a circle acting on R3R3 via rotation around a fixed line. We extend our results to the settings of arbitrary real hyperplane arrangements (the aforementioned theorems correspond to the braid arrangement) as well as oriented matroids.