Abstract
This chapter discusses the Chern character for discrete groups. Hj (X;Q) is the j-th Cech cohomology group of X with coefficients the rational numbers Q. The key property of this classical Chern character is that it is a rational isomorphism. Cyclic cohomology can be used to define the delocalized equivariant cohomology of X. The traditional homotopy quotient Chern character gives a map, which is always surjective, for compact X. The chapter also discusses twisted homology and K homology. K homology is the homology theory associated to the Z × BU spectrum. A concrete realization of this theory is obtained by using the K-cycle definition.
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