A Suspension Theorem for Continuous Trace C ∗ -Algebras

Abstract

Let R be a stable continuous trace C*-algebra with spectrum Y. We prove that the natural suspension map S*: [CO(X), _q] -g [CO(X) ? CO(Rt), q ? CO(R)] is a bijection, provided that both X and Y are locally compact connected spaces whose one-point compactifications have the homotopy type of a finite CW-complex and X is noncompact. This is used to compute the second homotopy group of g in terms of K-theory. That is, [Co(R2), _] = Ko(_o), where Ro is a maximal ideal of R if Y is compact, and Ro = R if Y is noncompact.