## 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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