Cohomology of classifying spaces of rank 3 Kac-Moody groups

2025/02/10 by Yangyang, Ruan, Xu-an, Zhao
#55N45 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.06169

Abstract

We represent the rational and mod p cohomology groups of classifying spaces of rank 3 Kac-Moody groups by a direct sum of the invariants of Weyl groups and their quotients. As an application, the authors conclude that there is a p-torsion for each prime p in the integral cohomology groups of classifying spaces of rank 3 Kac-Moody groups. We also determine the ring structure of the rational cohomology with one exception case.

Related

• The rational cohomology groups of the classifying spaces of Kac-Moody groups
• Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds
• On the Topology of Kac-Moody groups
• Weyl group invariants
• The cohomology rings of rank 3 simple groups are Cohen-Macaulay