Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583598 | Journal of Algebra | 2017 | 20 Pages |
Abstract
The cohomology of the configuration space of n points in R3 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 R1. Along the way, we give a presentation of the equivariant cohomology ring of the R3 configuration space with respect to a circle acting on R3 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Daniel Moseley,