Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds

2013/01/12 by Zhao Xu-an, Xuan Zhao, Jin Chunhua +4 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT

paper · pdf · doi:10.48550/arxiv.1301.2647

10 pages

arxiv created 2013/01/12 · openalex publication_date 2013/01/12 · arxiv updated 2013/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds. By extracting the information of cohomology from the Poincaré series, we are able to determine the rational cohomology rings of Kac-Moody groups and their flag manifolds. Since Kac-Moody groups and their flag manifolds are rational formal, we also determine their rational homotopy groups and rational homotopy types.

Cited by

• The ranks of homotopy groups of Kac-Moody groups

Related

• The rational cohomology groups of the classifying spaces of Kac-Moody groups
• The ranks of homotopy groups of Kac-Moody groups
• Cohomology of classifying spaces of rank 3 Kac-Moody groups
• On the Topology of Kac-Moody groups
• Computation of generalized equivariant cohomologies of Kac-Moody flag varieties