Homology of algebras of families of pseudodifferential operators

Details Homology of algebras of families of pseudodifferential operators Homology of algebras of families of pseudodifferential operators

2002-01-21

arxiv.org/abs/math/0201198v1

Mathematics

K-Theory and Homology

29 pages, LaTeX

Scientific paper

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 deduce an identification of the space of residue traces on fibrations by manifolds with corners. In the process, we prove several general results about algebras of complete symbols on manifolds with corners.

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