Equivariant cohomology and the Varchenko-Gelfand filtration

JOURNAL OF ALGEBRA

卷:472

Article

Moseley, Daniel¹ 

[1] Jacksonville Univ, 2800 Univ Blvd N, Jacksonville, FL 32211 USA

关键词: Hyperplane arrangements;    Equivariant cohomology;    Representation theory;    Configuration space;    Oriented matroids;   

DOI  :  10.1016/j.jalgebra.2016.10.010

来源: Elsevier

【 摘 要 】

The cohomology of the configuration space of n points in R-3 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 R-1. Along the way, we give a presentation of the equivariant cohomology ring of the R-3 configuration space with respect to a circle acting on R-3 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free