Homology of algebras of families of pseudodifferential operators

摘要

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology degenerates at E-2 and converges to Hochschild homology. As a byproduct, we identify the space of residue traces on fibrations by manifolds with corners. In the process, we prove some structural results about algebras of complete symbols on manifolds with corners. (C) 2003 Elsevier Inc. All rights reserved. [References: 51]