MAPPING THE HOMOLOGY OF A GROUP TO THE K-THEORY OF ITS C*-ALGEBRA

摘要

For a CW-complex X and for 0 ≤ j ≤ 2, we construct natural homomorphisms β_j~X : H_j(X; Z) → K_j(X) that are rationally right-inverses of the Chern character. We show that β_j~X is injective for j = 0 and j = 1. The case j = 3 is treated using Z[1/2]-coefficients. The study of these maps is motivated by the connection with the Baum-Connes conjecture on the K-theory of group C*-algebras.