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Homologie cyclique, caractère de Chern et lemme de perturbation. (Cyclic homology, Chern character and perturbation lemma). (French) Zbl 0691.18002

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

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
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