Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups
K-Theory and Homology
2007-05-23 v2 Algebraic Topology
Abstract
We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and cocompact discrete subgroups of connected Lie groups satisfy this assumption. The answer is given in terms of the group cohomology of G and of the centralizers of finite cyclic subgroups of prime power order. We also analyze the multiplicative structure.
Cite
@article{arxiv.math/0507237,
title = {Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups},
author = {Wolfgang Lueck},
journal= {arXiv preprint arXiv:math/0507237},
year = {2007}
}
Comments
35 pages Added two references and two sentences after Theorem 0.3