Cohomology of classifying spaces of rank 3 Kac-Moody groups

Ruan Yangyang; Zhao Xu-an

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arXiv · 2502.06169

Cohomology of classifying spaces of rank 3 Kac-Moody groups

Ruan Yangyang·Zhao Xu-an

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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.

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Ruan Yangyang, Zhao Xu-an. 2025-02-10. Cohomology of classifying spaces of rank 3 Kac-Moody groups. https://arxiv.org/abs/2502.06169

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