Steenrod operations on the Chow ring of a classifying space

2004/03/24 by Pierre Guillot, Guillot, Pierre
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AG #math.AT

paper · pdf · doi:10.48550/arxiv.math/0403415

32 pages, uses elsart.cls, submitted to Adv. Math

arxiv created 2004/03/24 · openalex publication_date 2004/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the Steenrod algebra to study CH^*BG, the mod p Chow ring of the classifying space of G. We describe a localization property which relates a given G to its elementary abelian subgroups, and we study a number of particular cases, namely symmetric groups and Chevalley groups. It turns out that the Chow rings of these groups are completely determined by the abelian subgroups and their fusion.

Related

• The Chow ring of a classifying space
• On the Chow Ring of the Classifying Space of some Chevalley Groups
• On the Chow rings of classifying spaces for classical groups
• The Chow Ring of the 2-Sylow Subgroup of GL(4,2)
• The Chow ring of Mbar_0,m(n, d)