## K-théorie multiplicative et homologie cyclique. (Multiplicative K- theory and cyclic homology).(French)Zbl 0601.18007

Let A be a locally convex topological algebra over a commutative ring containing the rational numbers. The author defines multiplicative K- theory groups $${\mathcal K}_ r(A)$$. Under suitable circumstances there is an exact sequence involving $${\mathcal K}_ r(A)$$, the topological K-theory $$K_ r^{top}(A)$$, and the cyclic homology of A. (The author gives a definition of cyclic homology using non-commutative differential forms.) Let $$K_ r(A)$$ be the Quillen algebraic K-theory of A. Then the homomorphism $$K_ r(A)\to K_ r^{top}(A)$$ factors through $${\mathcal K}_ r(A)$$.
Reviewer: R.J.Steiner

### MSC:

 18F25 Algebraic $$K$$-theory and $$L$$-theory (category-theoretic aspects) 55N15 Topological $$K$$-theory 46L80 $$K$$-theory and operator algebras (including cyclic theory)