A characterization of semiprojectivity for subhomogeneous \(C^*\)-algebras (Q321889)

Summary: We study semiprojective, subhomogeneous \(C^*\)-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous \(C^*\)-algebras: one in terms of their primitive ideal spaces and one by means of special direct limit structures over one-dimensional NCCW complexes. These results are obtained by working out several new permanence results for semiprojectivity, including a complete description of its behavior with respect to extensions by homogeneous \(C^*\)-algebras.