2009/05/19 by Pierre Guillot, Guillot, Pierre · 1 citation
Mathematics · #14C15 #20J06 #57R20 #65K05 #Advanced Combinatorial Mathematics #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:14C15 #msc:20J06 #msc:57R20 #msc:65K05
paper · pdf · doi:10.48550/arxiv.0905.3121
To appear in Ann. Inst. Fourier
arxiv created 2009/05/19 · openalex publication_date 2009/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet). Next, we give an application: thanks to the new information gathered, we can in many cases determine which cohomology classes are supported by algebraic varieties.