Homology of algebras of families of pseudodifferential operators

2002/01/21 by Moulay Tahar Benameur, Moulay Benameur, Benameur, Moulay +2
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.KT #math.OA

paper · pdf · doi:10.48550/arxiv.math/0201198

29 pages, LaTeX

arxiv created 2002/01/21 · arxiv updated 2009/11/30

Abstract

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 E² 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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