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Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups

Wolfgang Lueck
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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.

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Wolfgang Lueck. 2005-07-15. Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups. https://arxiv.org/abs/math/0507237

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