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The homology of algebras of pseudo-differential symbols and the noncommutative residue. (English) Zbl 0646.58026
The Hochschild and cyclic homology groups of the algebra of pseudo- differential symbols \(\Psi^{\infty}(M)/\Psi^{-\infty}(M)\) on a smooth m-dimensional manifold M are calculated; the main result is that \(HH_*(\Psi^{\infty}(M)/\Psi^{-\infty}(M))=H^{2n-*}(S\quad *M\times {\mathbb{S}}^ 1,{\mathbb{C}}),\) \(HC_*(\Psi^{\infty}(M)/\Psi^{- \infty}(M))=H^{2n-*}(S^*M\times {\mathbb{S}}^ 1,{\mathbb{C}})[u].\)
Reviewer: V.Ivrij

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
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