Sur la K-theorie multiplicative, by Max Karoubi

In this paper we introduce a new type of K-theory, called "multiplicative K-theory" kn(A) for A a Frechet algebra, which is intermediary between algebraic K-theory, denoted Kn(A), and topological K-theory, denoted Kntop(A). This new theory is computable in terms of Kntop(A) and cyclic homology HC*(A). The homomorphism from Kn(A) to kn(A) we define in the paper detects all known primary and secondary characterictic classes from algebraic K-theory to cyclic homology (for example the Borel regulator if A = the field of complex numbers). It is related to the multiplicative character of a Fredholm module defined previously by A. Connes and the author.

This paper has appeared in Proceedings of the Cyclic cohomology and Noncommutative conference, Fields Institute Communications, Vol. 17, American Mathematical Society (1997).

Max Karoubi <>