Kassel, Christian Homologie cyclique, caractère de Chern et lemme de perturbation. (Cyclic homology, Chern character and perturbation lemma). (French) Zbl 0691.18002 J. Reine Angew. Math. 408, 159-180 (1990). Using a perturbation lemma, we construct explicitly two-way chain maps between the various chain complexes defining cyclic homology. We derive several consequences, including an S operator on Connes’ cyclic complex, a new definition of bivariant cyclic cohomology and complete formulas for the Chern character on the algebraic \(K_ 0\)- and \(K_ 1\)-groups. Reviewer: C.Kassel Cited in 2 ReviewsCited in 24 Documents MSC: 18G35 Chain complexes (category-theoretic aspects), dg categories 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) 55U15 Chain complexes in algebraic topology Keywords:perturbation lemma; two-way chain maps; chain complexes; cyclic homology; cyclic complex; bivariant cyclic cohomology; Chern character; algebraic \(K_ 0\)- and \(K_ 1\)-groups PDFBibTeX XMLCite \textit{C. Kassel}, J. Reine Angew. Math. 408, 159--180 (1990; Zbl 0691.18002) Full Text: DOI Crelle EuDML