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Representations and $K$-theory of Discrete Groups

Alejandro Adem
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Abstract

Let $Γ$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $Γ$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(BΓ)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $Γ$.

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Alejandro Adem. 1993-01-01. Representations and $K$-theory of Discrete Groups. https://doi.org/10.1007/bf01232678

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