Topological K-(co-)homology of Classifying Spaces of Discrete Groups
نویسنده
چکیده
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction EG×G X of a proper G-CW -complex X satisfying certain finiteness conditions. In particular we give formulas computing the topological K-(co)homology K∗(BG) and K(BG) up to finite abelian torsion groups. They apply for instance to arithmetic groups, word hyperbolic groups, mapping class groups and discrete cocompact subgroups of almost connected Lie groups. For finite groups G these formulas are sharp. The main new tools we use for the K-theory calculation are a Cocompletion Theorem and Equivariant Universal Coefficient Theorems which are of independent interest. In the case where G is a finite group these theorems reduce to well-known results of Greenlees and Bökstedt.
منابع مشابه
Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups
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 ...
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تاریخ انتشار 2010