Title: Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups
Author: Wolfgang Lueck
AMS Classification Numbers: 55N15
Address: Wolfgang Lueck
Mathematisches Institut der Westfaelischen Wilhelms-Universitaet
Einsteinstr. 62
48149 Muenster
Germany
Email: lueck@math.uni-muenster.de
xxx-archive: KT/0507237
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.