The rational cohomology groups of the classifying spaces of Kac-Moody groups

2021/12/19 by Xuan Zhao, Xu-an, Zhao, Hongzhu, Gao +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2112.10069

openalex publication_date 2021/12/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we compute the rational cohomology groups of the classifying space of a simply connected Kac-Moody group of infinite type. The fundamental principle is "from finite to infinite". That is, for a Kac-Moody group G(A) of infinite type, the input data for computation are the rational cohomology of classifying spaces of parabolic subgroups of G(A)(which are of finite type), and the homomorphisms induced by inclusions of these subgroups. In some special cases, we can further determine the cohomology rings. Our method also applies to study the mod p cohomology of the classifying spaces of Kac-Moody groups.

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