On some applications of unstable Adams operations to the topology of Kac-Moody groups

TL;DR

This paper investigates the cohomology of classifying spaces of topological Kac-Moody groups using unstable Adams operations, showing spectral sequence collapse at almost all primes and deriving significant topological consequences.

Contribution

It applies unstable Adams operations to analyze spectral sequences, demonstrating their collapse and absence of extension problems for Kac-Moody groups at almost all primes.

Findings

Spectral sequences collapse at almost all primes.

No additive extension problems in the cohomology.

Describes consequences for the topology of Kac-Moody groups.

Abstract

Localized at almost all primes, we describe the structure of differentials in several important spectral sequences that compute the cohomology of classifying spaces of topological Kac-Moody groups. In particular, we show that for all but a finite set of primes, these spectral sequences collapse and that there are no additive extension problems. We also describe some appealing consequences of these results. The main tool is the use of the naturality properties of unstable Adams operations on these classifying spaces.