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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Representations and $ K$-theory of discrete groups

Author: Alejandro Adem
Journal: Bull. Amer. Math. Soc. 28 (1993), 95-98
MSC: Primary 55R35; Secondary 19L99, 20C99
MathSciNet review: 1168513
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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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