Wodzicki, Mariusz Cyclic homology of differential operators. (English) Zbl 0635.18010 Duke Math. J. 54, 641-647 (1987). Der Verf. zeigt, wie man für eine kompakte \(C^{\infty}\) Mannigfaltigkeit X die Hochschild- und die zyklische Homologie der Algebra der Differentialoperatoren auf X durch die De Rham Kohomologie von X ausdrücken kann. Entsprechende Ergebnisse gelten für Steinsche Mannigfaltigkeiten und für glatte affine Varietäten in der Charakteristik 0. Reviewer: K.Lamotke Cited in 3 ReviewsCited in 16 Documents MSC: 18G40 Spectral sequences, hypercohomology 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 58A12 de Rham theory in global analysis 14F40 de Rham cohomology and algebraic geometry 55N35 Other homology theories in algebraic topology Keywords:cyclic homology; Connes sequence; spectral sequence; differential operator; de Rham cohomology; Stein manifold; algebra of differential operators PDFBibTeX XMLCite \textit{M. Wodzicki}, Duke Math. J. 54, 641--647 (1987; Zbl 0635.18010) Full Text: DOI References: [1] J.-L. Brylinski, A differential complex for Poisson manifolds , preprint IHES, 1986. · Zbl 0634.58029 [2] B. B. Feigin and B. B. Tsygan, Cohomology of Lie algebras of generalized Jacobi matrices , Funktsional. Anal. i Prilozhen. 17 (1983), no. 2, 86-87. · Zbl 0544.17011 [3] G. Hochschild, B. Kostant, and A. Rosenberg, Differential forms on regular affine algebras , Trans. Amer. Math. Soc. 102 (1962), 383-408. · Zbl 0102.27701 [4] A. Ja. Helemskiĭ, Homological methods in the holomorphic calculus of several operators in Banach space, after Taylor , Uspekhi Mat. Nauk 36 (1981), no. 1(217), 127-172, 248. · Zbl 0495.46047 [5] J.-L. Loday and D. Quillen, Cyclic homology and the Lie algebra homology of matrices , Comment. Math. Helv. 59 (1984), no. 4, 569-591. · Zbl 0565.17006 [6] T. Masuda, Duality for differential crossed product and its periodic cyclic homology , preprint, IHES, 1985. · Zbl 0595.16023 [7] J. L. Taylor, Homology and cohomology for topological algebras , Advances in Math. 9 (1972), 137-182. · Zbl 0271.46040 [8] M. Wodzicki, Noncommutative residue. I. Fundamentals , \(K\)-theory, arithmetic and geometry (Moscow, 1984-1986) ed. Yu. I. Manin, Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 320-399. · Zbl 0649.58033 [9] M. Wodzicki, Noncommutative residue. Chapter IV. Homology of algebras of differential operators and symbols , (in preparation). · Zbl 1246.58024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.