Discrete approximations for complex Kac-Moody groups
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.
Cite
@article{arxiv.1209.0937,
title = {Discrete approximations for complex Kac-Moody groups},
author = {John D. Foley},
journal= {arXiv preprint arXiv:1209.0937},
year = {2015}
}
Comments
New title and revised introduction, references added; results and proofs unchanged, 31 pages, 1 figure