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arXiv · 1209.0937

Discrete approximations for complex Kac-Moody groups

John D. Foley
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Abstract

We construct a map from the classifying space of a discrete Kac-Moody group over the algebraic closure of the field with p elements to the classifying space of a complex topological Kac-Moody group and prove that it is a homology equivalence at primes q different from p. This generalises a classical result of Quillen-Friedlander-Mislin for Lie groups. As an application, we construct unstable Adams operations for general Kac-Moody groups compatible with the Frobenius homomorphism. In contrast to the Lie case, the homotopy fixed points of these unstable Adams operations cannot be realized at q as the classifying spaces of Kac-Moody groups over finite fields. Our results rely on new integral homology decompositions for certain infinite dimensional unipotent subgroups of discrete Kac-Moody groups.

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John D. Foley. 2014-08-26. Discrete approximations for complex Kac-Moody groups. https://doi.org/10.1016/j.aim.2014.09.015

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