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Equivariant cohomology and the Varchenko–Gelfand filtration.
- Source :
-
Journal of Algebra . Feb2017, Vol. 472, p95-114. 20p. - Publication Year :
- 2017
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 472
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 120322094
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2016.10.010