Rational computations of the topological K-theory of classifying spaces of discrete groups

Wolfgang Lück

Type: Article

Publication Date: 2007-01-26

Citations: 22

DOI: https://doi.org/10.1515/crelle.2007.078

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.

Locations

arXiv (Cornell University) - PDF
Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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