Representations and $K$-theory of Discrete Groups

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 $\Gamma$.

4 pages

Cited by in corpus (7)

• K-theory for ring C*-algebras - the case of number fields with higher roots of unity
• Yang-Mills theory over surfaces and the Atiyah-Segal theorem
• Topological K-(co-)homology of classifying spaces of discrete groups
• Equivariant $K$-homology for hyperbolic reflection groups
• Rational equivariant K-homology of low dimensional groups
• Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups
• The Burnside Ring and Equivariant Stable Cohomotopy for Infinite Groups