Representations and 𝐾-theory of discrete groups

Adem, Alejandro

doi:10.1090/S0273-0979-1993-00347-1

Representations and $K$-theory of discrete groups
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by Alejandro Adem PDF

Bull. Amer. Math. Soc. 28 (1993), 95-98 Request permission

Abstract:

Let $\Gamma$ 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 $\Gamma$, 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 $K^{\ast }(B\Gamma )$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $\Gamma$.

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